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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.quat_mem_fun"></a><a class="link" href="quat_mem_fun.html" title="Quaternion Member Functions">Quaternion Member Functions</a>
  28 </h2></div></div></div>
  29 <h4>
  30 <a name="math_toolkit.quat_mem_fun.h0"></a>
  31       <span class="phrase"><a name="math_toolkit.quat_mem_fun.constructors"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.constructors">Constructors</a>
  32     </h4>
  33 <p>
  34       Template version:
  35     </p>
  36 <pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">quaternion</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
  37 <span class="keyword">explicit</span> <span class="identifier">quaternion</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="identifier">T</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="identifier">T</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="identifier">T</span><span class="special">&gt;());</span>
  38 <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>
  39 <span class="keyword">explicit</span> <span class="identifier">quaternion</span><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_recopier</span><span class="special">);</span>
  40 </pre>
  41 <p>
  42       Float specialization version:
  43     </p>
  44 <pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">quaternion</span><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>
  45 <span class="keyword">explicit</span> <span class="identifier">quaternion</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">z0</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>
  46 <span class="keyword">explicit</span> <span class="identifier">quaternion</span><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>
  47 <span class="keyword">explicit</span> <span class="identifier">quaternion</span><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>
  48 </pre>
  49 <p>
  50       Double specialization version:
  51     </p>
  52 <pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">quaternion</span><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>
  53 <span class="keyword">explicit</span> <span class="identifier">quaternion</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">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>
  54 <span class="keyword">explicit</span> <span class="identifier">quaternion</span><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>
  55 <span class="keyword">explicit</span> <span class="identifier">quaternion</span><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>
  56 </pre>
  57 <p>
  58       Long double specialization version:
  59     </p>
  60 <pre class="programlisting"><span class="keyword">explicit</span> <span class="identifier">quaternion</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_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>
  61 <span class="keyword">explicit</span> <span class="identifier">quaternion</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">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>
  62 <span class="keyword">explicit</span> <span class="identifier">quaternion</span><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>
  63 <span class="keyword">explicit</span> <span class="identifier">quaternion</span><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>
  64 </pre>
  65 <p>
  66       A default constructor is provided for each form, which initializes each component
  67       to the default values for their type (i.e. zero for floating numbers). This
  68       constructor can also accept one to four base type arguments. A constructor
  69       is also provided to build quaternions from one or two complex numbers sharing
  70       the same base type. The unspecialized template also sports a templarized copy
  71       constructor, while the specialized forms have copy constructors from the other
  72       two specializations, which are explicit when a risk of precision loss exists.
  73       For the unspecialized form, the base type's constructors must not throw.
  74     </p>
  75 <p>
  76       Destructors and untemplated copy constructors (from the same type) are provided
  77       by the compiler. Converting copy constructors make use of a templated helper
  78       function in a "detail" subnamespace.
  79     </p>
  80 <h4>
  81 <a name="math_toolkit.quat_mem_fun.h1"></a>
  82       <span class="phrase"><a name="math_toolkit.quat_mem_fun.other_member_functions"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.other_member_functions">Other
  83       member functions</a>
  84     </h4>
  85 <h5>
  86 <a name="math_toolkit.quat_mem_fun.h2"></a>
  87       <span class="phrase"><a name="math_toolkit.quat_mem_fun.real_and_unreal_parts"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.real_and_unreal_parts">Real
  88       and Unreal Parts</a>
  89     </h5>
  90 <pre class="programlisting"><span class="identifier">T</span>             <span class="identifier">real</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  91 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">unreal</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
  92 </pre>
  93 <p>
  94       Like complex number, quaternions do have a meaningful notion of "real
  95       part", but unlike them there is no meaningful notion of "imaginary
  96       part". Instead there is an "unreal part" which itself is a quaternion,
  97       and usually nothing simpler (as opposed to the complex number case). These
  98       are returned by the first two functions.
  99     </p>
 100 <h5>
 101 <a name="math_toolkit.quat_mem_fun.h3"></a>
 102       <span class="phrase"><a name="math_toolkit.quat_mem_fun.individual_real_components"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_real_components">Individual
 103       Real Components</a>
 104     </h5>
 105 <pre class="programlisting"><span class="identifier">T</span> <span class="identifier">R_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 106 <span class="identifier">T</span> <span class="identifier">R_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 107 <span class="identifier">T</span> <span class="identifier">R_component_3</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 108 <span class="identifier">T</span> <span class="identifier">R_component_4</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 109 </pre>
 110 <p>
 111       A quaternion having four real components, these are returned by these four
 112       functions. Hence real and R_component_1 return the same value.
 113     </p>
 114 <h5>
 115 <a name="math_toolkit.quat_mem_fun.h4"></a>
 116       <span class="phrase"><a name="math_toolkit.quat_mem_fun.individual_complex_components"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.individual_complex_components">Individual
 117       Complex Components</a>
 118     </h5>
 119 <pre class="programlisting"><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="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">C_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 120 <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="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">C_component_2</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
 121 </pre>
 122 <p>
 123       A quaternion likewise has two complex components, and as we have seen above,
 124       for any quaternion <span class="emphasis"><em><code class="literal">q = &#945; + &#946;i + &#947;j + &#948;k</code></em></span> we also have
 125       <span class="emphasis"><em><code class="literal">q = (&#945; + &#946;i) + (&#947; + &#948;i)j </code></em></span>. These functions return them.
 126       The real part of <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">C_component_1</span><span class="special">()</span></code>
 127       is the same as <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code>.
 128     </p>
 129 <h4>
 130 <a name="math_toolkit.quat_mem_fun.h5"></a>
 131       <span class="phrase"><a name="math_toolkit.quat_mem_fun.quaternion_member_operators"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.quaternion_member_operators">Quaternion
 132       Member Operators</a>
 133     </h4>
 134 <h5>
 135 <a name="math_toolkit.quat_mem_fun.h6"></a>
 136       <span class="phrase"><a name="math_toolkit.quat_mem_fun.assignment_operators"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.assignment_operators">Assignment
 137       Operators</a>
 138     </h5>
 139 <pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</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>
 140 <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>
 141 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">=</span> <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>
 142 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span><span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
 143 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</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="identifier">T</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>
 144 </pre>
 145 <p>
 146       These perform the expected assignment, with type modification if necessary
 147       (for instance, assigning from a base type will set the real part to that value,
 148       and all other components to zero). For the unspecialized form, the base type's
 149       assignment operators must not throw.
 150     </p>
 151 <h5>
 152 <a name="math_toolkit.quat_mem_fun.h7"></a>
 153       <span class="phrase"><a name="math_toolkit.quat_mem_fun.addition_operators"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.addition_operators">Addition
 154       Operators</a>
 155     </h5>
 156 <pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">T</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="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</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="identifier">T</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="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">+=</span> <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 </pre>
 161 <p>
 162       These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)+</span><span class="identifier">rhs</span></code>
 163       and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>.
 164       The unspecialized form has exception guards, which the specialized forms do
 165       not, so as to insure exception safety. For the unspecialized form, the base
 166       type's assignment operators must not throw.
 167     </p>
 168 <h5>
 169 <a name="math_toolkit.quat_mem_fun.h8"></a>
 170       <span class="phrase"><a name="math_toolkit.quat_mem_fun.subtraction_operators"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.subtraction_operators">Subtraction
 171       Operators</a>
 172     </h5>
 173 <pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span>
 174 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</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="identifier">T</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>
 175 <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>
 176 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">-=</span> <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>
 177 </pre>
 178 <p>
 179       These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)-</span><span class="identifier">rhs</span></code>
 180       and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>.
 181       The unspecialized form has exception guards, which the specialized forms do
 182       not, so as to insure exception safety. For the unspecialized form, the base
 183       type's assignment operators must not throw.
 184     </p>
 185 <h5>
 186 <a name="math_toolkit.quat_mem_fun.h9"></a>
 187       <span class="phrase"><a name="math_toolkit.quat_mem_fun.multiplication_operators"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.multiplication_operators">Multiplication
 188       Operators</a>
 189     </h5>
 190 <pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span>
 191 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</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="identifier">T</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>
 192 <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>
 193 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">*=</span> <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>
 194 </pre>
 195 <p>
 196       These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">rhs</span></code>
 197       <span class="bold"><strong>in this order</strong></span> (order is important as multiplication
 198       is not commutative for quaternions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception guards,
 199       which the specialized forms do not, so as to insure exception safety. For the
 200       unspecialized form, the base type's assignment operators must not throw.
 201     </p>
 202 <h5>
 203 <a name="math_toolkit.quat_mem_fun.h10"></a>
 204       <span class="phrase"><a name="math_toolkit.quat_mem_fun.division_operators"></a></span><a class="link" href="quat_mem_fun.html#math_toolkit.quat_mem_fun.division_operators">Division
 205       Operators</a>
 206     </h5>
 207 <pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span>
 208 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</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="identifier">T</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>
 209 <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>
 210 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">/=</span> <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>
 211 </pre>
 212 <p>
 213       These perform the mathematical operation <code class="computeroutput"><span class="special">(*</span><span class="keyword">this</span><span class="special">)*</span><span class="identifier">inverse_of</span><span class="special">(</span><span class="identifier">rhs</span><span class="special">)</span></code>
 214       <span class="bold"><strong>in this order</strong></span> (order is important as multiplication
 215       is not commutative for quaternions) and store the result in <code class="computeroutput"><span class="special">*</span><span class="keyword">this</span></code>. The unspecialized form has exception guards,
 216       which the specialized forms do not, so as to insure exception safety. For the
 217       unspecialized form, the base type's assignment operators must not throw.
 218     </p>
 219 </div>
 220 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 221 <td align="left"></td>
 222 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
 223       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
 224       Holin, Bruno Lalande, John Maddock, Johan R&#229;de, Gautam Sewani, Benjamin Sobotta,
 225       Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
 226         Distributed under the Boost Software License, Version 1.0. (See accompanying
 227         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>)
 228       </p>
 229 </div></td>
 230 </tr></table>
 231 <hr>
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