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  27 <a name="math_toolkit.spec"></a><a class="link" href="spec.html" title="Quaternion Specializations">Quaternion Specializations</a>
  28 </h2></div></div></div>
  29 <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>
  30
  31 <span class="keyword">template</span><span class="special">&lt;&gt;</span>
  32 <span class="keyword">class</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>
  33 <span class="special">{</span>
  34 <span class="keyword">public</span><span class="special">:</span>
  35    <span class="keyword">typedef</span> <span class="keyword">float</span> <a class="link" href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
  36
  37    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
  38    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;());</span>
  39    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
  40    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
  41
  42    <span class="keyword">float</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  43    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>      <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  44    <span class="keyword">float</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  45    <span class="keyword">float</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  46    <span class="keyword">float</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  47    <span class="keyword">float</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  48    <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  49    <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  50
  51    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
  52    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
  53    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
  54    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
  55    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
  56
  57    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  58    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  59    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
  60    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  61
  62    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  63    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  64    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
  65    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  66
  67    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  68    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  69    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
  70    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  71
  72    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  73    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  74    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
  75    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
  76 <span class="special">};</span>
  77 </pre>
  78 <a name="math_quaternion_double"></a><pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;&gt;</span>
  79 <span class="keyword">class</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>
  80 <span class="special">{</span>
  81 <span class="keyword">public</span><span class="special">:</span>
  82    <span class="keyword">typedef</span> <span class="keyword">double</span> <a class="link" href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
  83
  84    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
  85    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>
  86    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
  87    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
  88
  89    <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  90    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>      <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  91    <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  92    <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  93    <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  94    <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  95    <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  96    <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  97
  98    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
  99    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 100    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
 101    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
 102    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
 103
 104    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 105    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 106    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 107    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 108
 109    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 110    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 111    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 112    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 113
 114    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 115    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 116    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 117    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 118
 119    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 120    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 121    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 122    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 123 <span class="special">};</span>
 124 </pre>
 125 <a name="math_quaternion_long_double"></a><pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;&gt;</span>
 126 <span class="keyword">class</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span>
 127 <span class="special">{</span>
 128 <span class="keyword">public</span><span class="special">:</span>
 129    <span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
 130
 131    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
 132    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;());</span>
 133    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
 134    <span class="keyword">explicit</span> <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
 135
 136    <span class="keyword">long</span> <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 137    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span>      <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 138    <span class="keyword">long</span> <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 139    <span class="keyword">long</span> <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 140    <span class="keyword">long</span> <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 141    <span class="keyword">long</span> <span class="keyword">double</span>                  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 142    <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span>  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 143    <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span>  <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 144
 145    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
 146    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 147    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
 148    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span>  <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
 149    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
 150
 151    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 152    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 153    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 154    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 155
 156    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 157    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 158    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 159    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 160
 161    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 162    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 163    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 164    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 165
 166    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 167    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 168    <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
 169    <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span>     <a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
 170 <span class="special">};</span>
 171
 172 <span class="special">}</span> <span class="comment">// namespace math</span>
 173 <span class="special">}</span> <span class="comment">// namespace boost</span>
 174 </pre>
 175 </div>
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