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  26. <div class="titlepage"><div><div><h2 class="title" style="clear: both">
    27. 

  27. <a name="math_toolkit.spec"></a><a class="link" href="spec.html" title="Quaternion Specializations">Quaternion Specializations</a>
    28. 

  28. </h2></div></div></div>
    29. 

  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. 

  30. 

  31. <span class="keyword">template</span><span class="special">&lt;&gt;</span>
    32. 

  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. 

  33. <span class="special">{</span>
    34. 

  34. <span class="keyword">public</span><span class="special">:</span>
    35. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  76. <span class="special">};</span>
    77. 

  77. </pre>
    78. 

  78. <a name="math_quaternion_double"></a><pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;&gt;</span>
    79. 

  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. 

  80. <span class="special">{</span>
    81. 

  81. <span class="keyword">public</span><span class="special">:</span>
    82. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  123. <span class="special">};</span>
    124. 

  124. </pre>
    125. 

  125. <a name="math_quaternion_long_double"></a><pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;&gt;</span>
    126. 

  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. 

  127. <span class="special">{</span>
    128. 

  128. <span class="keyword">public</span><span class="special">:</span>
    129. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  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. 

  170. <span class="special">};</span>
    171. 

  171. 

  172. <span class="special">}</span> <span class="comment">// namespace math</span>
    173. 

  173. <span class="special">}</span> <span class="comment">// namespace boost</span>
    174. 

  174. </pre>
    175. 

  175. </div>
    176. 

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    177. 

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    178. 

  178. <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
    179. 

  179.       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
    180. 

  180.       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
    181. 

  181.       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
    182. 

  182.       Daryle Walker and Xiaogang Zhang<p>
    183. 

  183.         Distributed under the Boost Software License, Version 1.0. (See accompanying
    184. 

  184.         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>)
    185. 

  185.       </p>
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