ceph/src/boost/libs/multiprecision/doc/html/boost_multiprecision/tut/misc/logged_adapter.html

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  25 <div class="section boost_multiprecision_tut_misc_logged_adaptor">
  26 <div class="titlepage"><div><div><h4 class="title">
  27 <a name="boost_multiprecision.tut.misc.logged_adaptor"></a><a class="link" href="logged_adaptor.html" title="logged_adaptor">logged_adaptor</a>
  28 </h4></div></div></div>
  29 <p>
  30           <code class="computeroutput"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">logged_adaptor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span></code>
  31         </p>
  32 <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">multiprecision</span><span class="special">{</span>
  33
  34 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">&gt;</span>
  35 <span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&amp;</span> <span class="identifier">result</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span>
  36 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  37 <span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&amp;</span> <span class="identifier">result1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">result2</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span>
  38
  39 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">&gt;</span>
  40 <span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&amp;</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span>
  41 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
  42 <span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&amp;</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span>
  43 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">&gt;</span>
  44 <span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&amp;</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">arg3</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span>
  45 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Backend</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">U</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">V</span><span class="special">&gt;</span>
  46 <span class="keyword">void</span> <span class="identifier">log_prefix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Backend</span><span class="special">&amp;</span> <span class="identifier">arg1</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">arg2</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">U</span><span class="special">&amp;</span> <span class="identifier">arg3</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">V</span><span class="special">&amp;</span> <span class="identifier">arg4</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">);</span>
  47
  48 <span class="keyword">template</span> <span class="special">&lt;</span><span class="identifier">Backend</span><span class="special">&gt;</span>
  49 <span class="keyword">class</span> <span class="identifier">logged_adaptor</span><span class="special">;</span>
  50
  51 <span class="special">}}</span> <span class="comment">// namespaces</span>
  52 </pre>
  53 <p>
  54           The <code class="computeroutput"><span class="identifier">logged_adaptor</span></code> type
  55           is used in conjunction with <code class="computeroutput"><span class="identifier">number</span></code>
  56           and some other backend type: it acts as a thin wrapper around some other
  57           backend to class <code class="computeroutput"><span class="identifier">number</span></code>
  58           and logs all the events that take place on that object. Before any number
  59           operation takes place, it calls <code class="computeroutput"><span class="identifier">log_prefix_event</span></code>
  60           with the arguments to the operation (up to 4), plus a string describing
  61           the operation. Then after the operation it calls <code class="computeroutput"><span class="identifier">log_postfix_event</span></code>
  62           with the result of the operation, plus a string describing the operation.
  63           Optionally, <code class="computeroutput"><span class="identifier">log_postfix_event</span></code>
  64           takes a second result argument: this occurs when the result of the operation
  65           is not a <code class="computeroutput"><span class="identifier">number</span></code>, for example
  66           when <code class="computeroutput"><span class="identifier">fpclassify</span></code> is called,
  67           <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> will
  68           be called with <code class="computeroutput"><span class="identifier">result1</span></code>
  69           being the argument to the function, and <code class="computeroutput"><span class="identifier">result2</span></code>
  70           being the integer result of <code class="computeroutput"><span class="identifier">fpclassify</span></code>.
  71         </p>
  72 <p>
  73           The default versions of <code class="computeroutput"><span class="identifier">log_prefix_event</span></code>
  74           and <code class="computeroutput"><span class="identifier">log_postfix_event</span></code> do
  75           nothing, it is therefore up to the user to overload these for the particular
  76           backend being observed.
  77         </p>
  78 <p>
  79           This type provides <code class="computeroutput"><span class="identifier">numeric_limits</span></code>
  80           support whenever the template argument Backend does so.
  81         </p>
  82 <p>
  83           This type is particularly useful when combined with an interval number
  84           type - in this case we can use <code class="computeroutput"><span class="identifier">log_postfix_event</span></code>
  85           to monitor the error accumulated after each operation. We could either
  86           set some kind of trap whenever the accumulated error exceeds some threshold,
  87           or simply print out diagnostic information. Using this technique we can
  88           quickly locate the cause of numerical instability in a particular routine.
  89           The following example demonstrates this technique in a trivial algorithm
  90           that deliberately introduces cancellation error:
  91         </p>
  92 <p>
  93 </p>
  94 <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">multiprecision</span><span class="special">/</span><span class="identifier">mpfi</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  95 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">logged_adaptor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  96 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
  97 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iomanip</span><span class="special">&gt;</span>
  98 <span class="comment">//</span>
  99 <span class="comment">// Begin by overloading log_postfix_event so we can capture each arithmetic event as it happens:</span>
 100 <span class="comment">//</span>
 101 <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">multiprecision</span><span class="special">{</span>
 102
 103 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">D</span><span class="special">&gt;</span>
 104 <span class="keyword">inline</span> <span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">D</span><span class="special">&gt;&amp;</span> <span class="identifier">val</span><span class="special">,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">)</span>
 105 <span class="special">{</span>
 106    <span class="comment">// Print out the (relative) diameter of the interval:</span>
 107    <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>
 108    <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">mpfr_float_backend</span><span class="special">&lt;</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">diam</span><span class="special">;</span>
 109    <span class="identifier">mpfi_diam</span><span class="special">(</span><span class="identifier">diam</span><span class="special">.</span><span class="identifier">backend</span><span class="special">().</span><span class="identifier">data</span><span class="special">(),</span> <span class="identifier">val</span><span class="special">.</span><span class="identifier">data</span><span class="special">());</span>
 110    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Diameter was "</span> <span class="special">&lt;&lt;</span> <span class="identifier">diam</span> <span class="special">&lt;&lt;</span> <span class="string">" after operation: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">event_description</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>
 111 <span class="special">}</span>
 112 <span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">unsigned</span> <span class="identifier">D</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 113 <span class="keyword">inline</span> <span class="keyword">void</span> <span class="identifier">log_postfix_event</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="identifier">D</span><span class="special">&gt;&amp;,</span> <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;,</span> <span class="keyword">const</span> <span class="keyword">char</span><span class="special">*</span> <span class="identifier">event_description</span><span class="special">)</span>
 114 <span class="special">{</span>
 115    <span class="comment">// This version is never called in this example.</span>
 116 <span class="special">}</span>
 117
 118 <span class="special">}}</span>
 119
 120
 121 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
 122 <span class="special">{</span>
 123    <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>
 124    <span class="keyword">typedef</span> <span class="identifier">number</span><span class="special">&lt;</span><span class="identifier">logged_adaptor</span><span class="special">&lt;</span><span class="identifier">mpfi_float_backend</span><span class="special">&lt;</span><span class="number">17</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">logged_type</span><span class="special">;</span>
 125    <span class="comment">//</span>
 126    <span class="comment">// Test case deliberately introduces cancellation error, relative size of interval</span>
 127    <span class="comment">// gradually gets larger after each operation:</span>
 128    <span class="comment">//</span>
 129    <span class="identifier">logged_type</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
 130    <span class="identifier">a</span> <span class="special">/=</span> <span class="number">10</span><span class="special">;</span>
 131
 132    <span class="keyword">for</span><span class="special">(</span><span class="keyword">unsigned</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="number">13</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
 133    <span class="special">{</span>
 134       <span class="identifier">logged_type</span> <span class="identifier">b</span> <span class="special">=</span> <span class="identifier">a</span> <span class="special">*</span> <span class="number">9</span><span class="special">;</span>
 135       <span class="identifier">b</span> <span class="special">/=</span> <span class="number">10</span><span class="special">;</span>
 136       <span class="identifier">a</span> <span class="special">-=</span> <span class="identifier">b</span><span class="special">;</span>
 137    <span class="special">}</span>
 138    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Final value was: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">a</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>
 139    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
 140 <span class="special">}</span>
 141 </pre>
 142 <p>
 143         </p>
 144 <p>
 145           When we examine program output we can clearly see that the diameter of
 146           the interval increases after each subtraction:
 147         </p>
 148 <p>
 149 </p>
 150 <pre class="programlisting"><span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 151 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Assignment</span> <span class="identifier">from</span> <span class="identifier">arithmetic</span> <span class="identifier">type</span>
 152 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.33681e-18</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 153 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 154 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">7.70988e-18</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 155 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.63735e-18</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 156 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.30104e-16</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 157 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 158 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.30104e-16</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 159 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.38537e-16</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 160 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.54788e-15</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 161 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 162 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.54788e-15</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 163 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.54863e-15</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 164 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.84164e-14</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 165 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 166 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.84164e-14</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 167 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.84221e-14</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 168 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.19962e-13</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 169 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 170 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.19962e-13</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 171 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">9.19966e-13</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 172 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.74793e-11</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 173 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 174 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.74793e-11</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 175 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.74793e-11</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 176 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">3.32107e-10</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 177 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 178 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">3.32107e-10</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 179 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">3.32107e-10</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 180 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">6.31003e-09</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 181 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 182 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">6.31003e-09</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 183 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">6.31003e-09</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 184 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.19891e-07</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 185 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 186 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.19891e-07</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 187 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">1.19891e-07</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 188 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.27792e-06</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 189 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 190 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.27792e-06</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 191 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">2.27792e-06</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 192 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.32805e-05</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 193 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 194 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.32805e-05</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 195 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">4.32805e-05</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 196 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.00082233</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 197 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 198 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.00082233</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 199 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.00082233</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 200 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.0156243</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 201 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="identifier">nan</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="identifier">Default</span> <span class="identifier">construct</span>
 202 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.0156243</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">*</span>
 203 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.0156243</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">/=</span>
 204 <span class="identifier">Diameter</span> <span class="identifier">was</span> <span class="number">0.296861</span> <span class="identifier">after</span> <span class="identifier">operation</span><span class="special">:</span> <span class="special">-=</span>
 205 <span class="identifier">Final</span> <span class="identifier">value</span> <span class="identifier">was</span><span class="special">:</span> <span class="special">{</span><span class="number">8.51569e-15</span><span class="special">,</span><span class="number">1.14843e-14</span><span class="special">}</span>
 206 </pre>
 207 <p>
 208         </p>
 209 </div>
 210 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 211 <td align="left"></td>
 212 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2012 John Maddock and Christopher Kormanyos<p>
 213         Distributed under the Boost Software License, Version 1.0. (See accompanying
 214         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>)
 215       </p>
 216 </div></td>
 217 </tr></table>
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