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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <a name="boost_quaternions.quaternions.non_mem"></a><a class="link" href="non_mem.html" title="Quaternion Non-Member Operators">Quaternion Non-Member
  28       Operators</a>
  29 </h3></div></div></div>
  30 <a name="boost_quaternions.quaternions.non_mem.unary_plus"></a><h5>
  31 <a name="id1038075"></a>
  32         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_plus">Unary Plus</a>
  33       </h5>
  34 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
  35 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">q</span><span class="special">);</span>
  36 </pre>
  37 <p>
  38         This unary operator simply returns q.
  39       </p>
  40 <a name="boost_quaternions.quaternions.non_mem.unary_minus"></a><h5>
  41 <a name="id1038179"></a>
  42         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_minus">Unary Minus</a>
  43       </h5>
  44 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
  45 <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">q</span><span class="special">);</span>
  46 </pre>
  47 <p>
  48         This unary operator returns the opposite of q.
  49       </p>
  50 <a name="boost_quaternions.quaternions.non_mem.binary_addition_operators"></a><h5>
  51 <a name="id1038285"></a>
  52         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">Binary
  53         Addition Operators</a>
  54       </h5>
  55 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>      <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
  56 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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>
  57 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
  58 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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>
  59 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
  60 </pre>
  61 <p>
  62         These operators return <code class="computeroutput"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">+=</span>
  63         <span class="identifier">rhs</span></code>.
  64       </p>
  65 <a name="boost_quaternions.quaternions.non_mem.binary_subtraction_operators"></a><h5>
  66 <a name="id1038927"></a>
  67         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">Binary
  68         Subtraction Operators</a>
  69       </h5>
  70 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>      <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
  71 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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>
  72 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
  73 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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>
  74 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
  75 </pre>
  76 <p>
  77         These operators return <code class="computeroutput"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">-=</span>
  78         <span class="identifier">rhs</span></code>.
  79       </p>
  80 <a name="boost_quaternions.quaternions.non_mem.binary_multiplication_operators"></a><h5>
  81 <a name="id1039561"></a>
  82         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">Binary
  83         Multiplication Operators</a>
  84       </h5>
  85 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>      <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
  86 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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>
  87 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
  88 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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>
  89 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
  90 </pre>
  91 <p>
  92         These operators return <code class="computeroutput"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">*=</span>
  93         <span class="identifier">rhs</span></code>.
  94       </p>
  95 <a name="boost_quaternions.quaternions.non_mem.binary_division_operators"></a><h5>
  96 <a name="id1040197"></a>
  97         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">Binary
  98         Division Operators</a>
  99       </h5>
 100 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>      <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
 101 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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>
 102 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
 103 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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>
 104 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</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">lhs</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">rhs</span><span class="special">);</span>
 105 </pre>
 106 <p>
 107         These operators return <code class="computeroutput"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">/=</span>
 108         <span class="identifier">rhs</span></code>. It is of course still an error
 109         to divide by zero...
 110       </p>
 111 <a name="boost_quaternions.quaternions.non_mem.equality_operators"></a><h5>
 112 <a name="id1040835"></a>
 113         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">Equality
 114         Operators</a>
 115       </h5>
 116 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>      <span class="keyword">bool</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">lhs</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">rhs</span><span class="special">);</span>
 117 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="keyword">bool</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">lhs</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>
 118 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="keyword">bool</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">lhs</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">rhs</span><span class="special">);</span>
 119 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="keyword">bool</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">lhs</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>
 120 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="keyword">bool</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">lhs</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">rhs</span><span class="special">);</span>
 121 </pre>
 122 <p>
 123         These return true if and only if the four components of <code class="computeroutput"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span></code> are
 124         equal to their counterparts in <code class="computeroutput"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">rhs</span><span class="special">)</span></code>. As
 125         with any floating-type entity, this is essentially meaningless.
 126       </p>
 127 <a name="boost_quaternions.quaternions.non_mem.inequality_operators"></a><h5>
 128 <a name="id1043620"></a>
 129         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">Inequality
 130         Operators</a>
 131       </h5>
 132 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>      <span class="keyword">bool</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">lhs</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">rhs</span><span class="special">);</span>
 133 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="keyword">bool</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">lhs</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>
 134 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="keyword">bool</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">lhs</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">rhs</span><span class="special">);</span>
 135 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="keyword">bool</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">lhs</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>
 136 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>  <span class="keyword">bool</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">lhs</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">rhs</span><span class="special">);</span>
 137 </pre>
 138 <p>
 139         These return true if and only if <code class="computeroutput"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">lhs</span><span class="special">)</span> <span class="special">==</span>
 140         <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(</span><span class="identifier">rhs</span><span class="special">)</span></code> is
 141         false. As with any floating-type entity, this is essentially meaningless.
 142       </p>
 143 <a name="boost_quaternions.quaternions.non_mem.stream_extractor"></a><h5>
 144 <a name="id1044220"></a>
 145         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_extractor">Stream
 146         Extractor</a>
 147       </h5>
 148 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
 149 <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">&gt;&gt;</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">is</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="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
 150 </pre>
 151 <p>
 152         Extracts a quaternion q of one of the following forms (with a, b, c and d
 153         of type <code class="computeroutput"><span class="identifier">T</span></code>):
 154       </p>
 155 <p>
 156         <code class="literal">a (a), (a,b), (a,b,c), (a,b,c,d) (a,(c)), (a,(c,d)), ((a)), ((a),c),
 157         ((a),(c)), ((a),(c,d)), ((a,b)), ((a,b),c), ((a,b),(c)), ((a,b),(c,d))</code>
 158       </p>
 159 <p>
 160         The input values must be convertible to <code class="computeroutput"><span class="identifier">T</span></code>.
 161         If bad input is encountered, calls <code class="computeroutput"><span class="identifier">is</span><span class="special">.</span><span class="identifier">setstate</span><span class="special">(</span><span class="identifier">ios</span><span class="special">::</span><span class="identifier">failbit</span><span class="special">)</span></code>
 162         (which may throw ios::failure (27.4.5.3)).
 163       </p>
 164 <p>
 165         <span class="bold"><strong>Returns:</strong></span> <code class="computeroutput"><span class="identifier">is</span></code>.
 166       </p>
 167 <p>
 168         The rationale for the list of accepted formats is that either we have a list
 169         of up to four reals, or else we have a couple of complex numbers, and in
 170         that case if it formated as a proper complex number, then it should be accepted.
 171         Thus potential ambiguities are lifted (for instance (a,b) is (a,b,0,0) and
 172         not (a,0,b,0), i.e. it is parsed as a list of two real numbers and not two
 173         complex numbers which happen to have imaginary parts equal to zero).
 174       </p>
 175 <a name="boost_quaternions.quaternions.non_mem.stream_inserter"></a><h5>
 176 <a name="id1044486"></a>
 177         <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_inserter">Stream
 178         Inserter</a>
 179       </h5>
 180 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
 181 <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">&lt;&lt;</span> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">os</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">q</span><span class="special">);</span>
 182 </pre>
 183 <p>
 184         Inserts the quaternion q onto the stream <code class="computeroutput"><span class="identifier">os</span></code>
 185         as if it were implemented as follows:
 186       </p>
 187 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
 188 <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">&lt;&lt;</span> <span class="special">(</span>
 189                <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span>
 190                <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">q</span><span class="special">)</span>
 191 <span class="special">{</span>
 192    <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostringstream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span>      <span class="identifier">s</span><span class="special">;</span>
 193
 194    <span class="identifier">s</span><span class="special">.</span><span class="identifier">flags</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">flags</span><span class="special">());</span>
 195    <span class="identifier">s</span><span class="special">.</span><span class="identifier">imbue</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">getloc</span><span class="special">());</span>
 196    <span class="identifier">s</span><span class="special">.</span><span class="identifier">precision</span><span class="special">(</span><span class="identifier">os</span><span class="special">.</span><span class="identifier">precision</span><span class="special">());</span>
 197
 198    <span class="identifier">s</span> <span class="special">&lt;&lt;</span> <span class="char">'('</span> <span class="special">&lt;&lt;</span> <span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 199             <span class="special">&lt;&lt;</span> <span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_2</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 200             <span class="special">&lt;&lt;</span> <span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_3</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">','</span>
 201             <span class="special">&lt;&lt;</span> <span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="char">')'</span><span class="special">;</span>
 202
 203    <span class="keyword">return</span> <span class="identifier">os</span> <span class="special">&lt;&lt;</span> <span class="identifier">s</span><span class="special">.</span><span class="identifier">str</span><span class="special">();</span>
 204 <span class="special">}</span>
 205 </pre>
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