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  25 </div>
  26 <div class="section">
  27 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  28 <a name="boost_units.Examples"></a><a class="link" href="Examples.html" title="Examples">Examples</a>
  29 </h2></div></div></div>
  30 <div class="toc"><dl class="toc">
  31 <dt><span class="section"><a href="Examples.html#boost_units.Examples.DimensionExample">Dimension Example</a></span></dt>
  32 <dt><span class="section"><a href="Examples.html#boost_units.Examples.UnitExample">Unit Example</a></span></dt>
  33 <dt><span class="section"><a href="Examples.html#boost_units.Examples.QuantityExample">Quantity Example</a></span></dt>
  34 <dt><span class="section"><a href="Examples.html#boost_units.Examples.KitchenSinkExample">Kitchen Sink
  35       Example using SI units</a></span></dt>
  36 <dt><span class="section"><a href="Examples.html#boost_units.Examples.ConversionExample">Conversion Example</a></span></dt>
  37 <dt><span class="section"><a href="Examples.html#boost_units.Examples.UDTExample">User Defined Types</a></span></dt>
  38 <dt><span class="section"><a href="Examples.html#boost_units.Examples.ComplexExample">Complex Example</a></span></dt>
  39 <dt><span class="section"><a href="Examples.html#boost_units.Examples.PerformanceExample">Performance
  40       Example</a></span></dt>
  41 <dt><span class="section"><a href="Examples.html#boost_units.Examples.RadarBeamHeightExample">Radar Beam
  42       Height</a></span></dt>
  43 <dt><span class="section"><a href="Examples.html#boost_units.Examples.HeterogeneousUnitExample">Heterogeneous
  44       Unit Example</a></span></dt>
  45 <dt><span class="section"><a href="Examples.html#boost_units.Examples.AbsoluteRelativeTemperatureExample">Absolute
  46       and Relative Temperature Example</a></span></dt>
  47 <dt><span class="section"><a href="Examples.html#boost_units.Examples.RuntimeConversionFactorExample">Runtime
  48       Conversion Factor Example</a></span></dt>
  49 <dt><span class="section"><a href="Examples.html#boost_units.Examples.UnitsWithNonbaseDimensions">Units
  50       with Non-base Dimensions</a></span></dt>
  51 <dt><span class="section"><a href="Examples.html#boost_units.Examples.OutputForCompositeUnits">Output
  52       for Composite Units</a></span></dt>
  53 <dt><span class="section"><a href="Examples.html#boost_units.Examples.autoscale">Automatically Scaled
  54       Units</a></span></dt>
  55 <dt><span class="section"><a href="Examples.html#boost_units.Examples.ConversionFactor">Conversion Factor</a></span></dt>
  56 <dt><span class="section"><a href="Examples.html#boost_units.Examples.RuntimeUnits">Runtime Units</a></span></dt>
  57 <dt><span class="section"><a href="Examples.html#boost_units.Examples.lambda">Interoperability with Boost.Lambda</a></span></dt>
  58 </dl></div>
  59 <div class="section">
  60 <div class="titlepage"><div><div><h3 class="title">
  61 <a name="boost_units.Examples.DimensionExample"></a><a class="link" href="Examples.html#boost_units.Examples.DimensionExample" title="Dimension Example">Dimension Example</a>
  62 </h3></div></div></div>
  63 <p>
  64         (<a href="../../../libs/units/example/dimension.cpp" target="_top">dimension.cpp</a>)
  65       </p>
  66 <p>
  67         By using MPL metafunctions and the template specializations for operations
  68         on composite dimensions (defined in <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.dimension_hpp" title="Header &lt;boost/units/dimension.hpp&gt;">boost/units/dimension.hpp</a></code>)
  69         it is possible to perform compile time arithmetic according to the dimensional
  70         analysis rules described <a class="link" href="Dimensional_Analysis.html" title="Dimensional Analysis">above</a>
  71         to produce new composite dimensions :
  72       </p>
  73 <p>
  74 </p>
  75 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">times</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">mass_dimension</span><span class="special">&gt;::</span><span class="identifier">type</span>   <span class="identifier">LM_type</span><span class="special">;</span>
  76 <span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">divides</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">time_dimension</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">L_T_type</span><span class="special">;</span>
  77 <span class="keyword">typedef</span> <span class="identifier">static_root</span><span class="special">&lt;</span>
  78     <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">divides</span><span class="special">&lt;</span><span class="identifier">energy_dimension</span><span class="special">,</span><span class="identifier">mass_dimension</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">,</span>
  79     <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;</span>
  80 <span class="special">&gt;::</span><span class="identifier">type</span>    <span class="identifier">V_type</span><span class="special">;</span>
  81 </pre>
  82 <p>
  83       </p>
  84 <p>
  85         outputting (with symbol demangling, implemented in <a href="../../../boost/units/detail/utility.hpp" target="_top">utility.hpp</a>)
  86       </p>
  87 <p>
  88 </p>
  89 <pre class="programlisting"><span class="identifier">length_dimension</span>  <span class="special">=</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">length_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">dimensionless_type</span><span class="special">&gt;</span>
  90 <span class="identifier">mass_dimension</span>    <span class="special">=</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">mass_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">dimensionless_type</span><span class="special">&gt;</span>
  91 <span class="identifier">time_dimension</span>    <span class="special">=</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">time_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">dimensionless_type</span><span class="special">&gt;</span>
  92 <span class="identifier">energy_dimension</span>  <span class="special">=</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">length_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">2l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">mass_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">time_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;-</span><span class="number">2l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">dimensionless_type</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span>
  93 <span class="identifier">LM_type</span>      <span class="special">=</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">length_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">mass_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">dimensionless_type</span><span class="special">&gt;</span> <span class="special">&gt;</span>
  94 <span class="identifier">L_T_type</span>     <span class="special">=</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">length_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">time_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;-</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">dimensionless_type</span><span class="special">&gt;</span> <span class="special">&gt;</span>
  95 <span class="identifier">V_type</span>       <span class="special">=</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">length_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">list</span><span class="special">&lt;</span><span class="identifier">dim</span><span class="special">&lt;</span><span class="identifier">time_base_dimension</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;-</span><span class="number">1l</span><span class="special">,</span> <span class="number">1l</span><span class="special">&gt;</span> <span class="special">&gt;,</span> <span class="identifier">dimensionless_type</span><span class="special">&gt;</span> <span class="special">&gt;</span>
  96 </pre>
  97 <p>
  98       </p>
  99 </div>
 100 <div class="section">
 101 <div class="titlepage"><div><div><h3 class="title">
 102 <a name="boost_units.Examples.UnitExample"></a><a class="link" href="Examples.html#boost_units.Examples.UnitExample" title="Unit Example">Unit Example</a>
 103 </h3></div></div></div>
 104 <p>
 105         (<a href="../../../libs/units/example/unit.cpp" target="_top">unit.cpp</a>)
 106       </p>
 107 <p>
 108         This example demonstrates the use of the simple but functional unit system
 109         implemented in <a href="../../../libs/units/example/test_system.hpp" target="_top">test_system.hpp</a>
 110       </p>
 111 <p>
 112 </p>
 113 <pre class="programlisting"><span class="keyword">const</span> <span class="identifier">length</span>                    <span class="identifier">L</span><span class="special">;</span>
 114 <span class="keyword">const</span> <span class="identifier">mass</span>                      <span class="identifier">M</span><span class="special">;</span>
 115 <span class="comment">// needs to be namespace-qualified because of global time definition</span>
 116 <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">test</span><span class="special">::</span><span class="identifier">time</span>  <span class="identifier">T</span><span class="special">;</span>
 117 <span class="keyword">const</span> <span class="identifier">energy</span>                    <span class="identifier">E</span><span class="special">;</span>
 118 </pre>
 119 <p>
 120       </p>
 121 <p>
 122         We can perform various algebraic operations on these units, resulting in
 123         the following output:
 124       </p>
 125 <p>
 126 </p>
 127 <pre class="programlisting"><span class="identifier">L</span>             <span class="special">=</span> <span class="identifier">m</span>
 128 <span class="identifier">L</span><span class="special">+</span><span class="identifier">L</span>           <span class="special">=</span> <span class="identifier">m</span>
 129 <span class="identifier">L</span><span class="special">-</span><span class="identifier">L</span>           <span class="special">=</span> <span class="identifier">m</span>
 130 <span class="identifier">L</span><span class="special">/</span><span class="identifier">L</span>           <span class="special">=</span> <span class="identifier">dimensionless</span>
 131 <span class="identifier">meter</span><span class="special">*</span><span class="identifier">meter</span>   <span class="special">=</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span>
 132 <span class="identifier">M</span><span class="special">*(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">T</span><span class="special">)*(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">T</span><span class="special">)</span> <span class="special">=</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span>
 133 <span class="identifier">M</span><span class="special">*(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">T</span><span class="special">)^</span><span class="number">2</span>     <span class="special">=</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span>
 134 <span class="identifier">L</span><span class="special">^</span><span class="number">3</span>           <span class="special">=</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span>
 135 <span class="identifier">L</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>       <span class="special">=</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>
 136 <span class="number">2</span><span class="identifier">vM</span>           <span class="special">=</span> <span class="identifier">kg</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>
 137 <span class="special">(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span><span class="identifier">vM</span>       <span class="special">=</span> <span class="identifier">kg</span><span class="special">^(</span><span class="number">2</span><span class="special">/</span><span class="number">3</span><span class="special">)</span>
 138 </pre>
 139 <p>
 140       </p>
 141 </div>
 142 <div class="section">
 143 <div class="titlepage"><div><div><h3 class="title">
 144 <a name="boost_units.Examples.QuantityExample"></a><a class="link" href="Examples.html#boost_units.Examples.QuantityExample" title="Quantity Example">Quantity Example</a>
 145 </h3></div></div></div>
 146 <p>
 147         (<a href="../../../libs/units/example/quantity.cpp" target="_top">quantity.cpp</a>)
 148       </p>
 149 <p>
 150         This example demonstrates how to use quantities of our toy unit system :
 151       </p>
 152 <p>
 153 </p>
 154 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="identifier">L</span> <span class="special">=</span> <span class="number">2.0</span><span class="special">*</span><span class="identifier">meters</span><span class="special">;</span>                     <span class="comment">// quantity of length</span>
 155 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">energy</span><span class="special">&gt;</span> <span class="identifier">E</span> <span class="special">=</span> <span class="identifier">kilograms</span><span class="special">*</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">seconds</span><span class="special">);</span>    <span class="comment">// quantity of energy</span>
 156 </pre>
 157 <p>
 158       </p>
 159 <p>
 160         giving us the basic quantity functionality :
 161       </p>
 162 <p>
 163 </p>
 164 <pre class="programlisting"><span class="identifier">L</span>                                 <span class="special">=</span> <span class="number">2</span> <span class="identifier">m</span>
 165 <span class="identifier">L</span><span class="special">+</span><span class="identifier">L</span>                               <span class="special">=</span> <span class="number">4</span> <span class="identifier">m</span>
 166 <span class="identifier">L</span><span class="special">-</span><span class="identifier">L</span>                               <span class="special">=</span> <span class="number">0</span> <span class="identifier">m</span>
 167 <span class="identifier">L</span><span class="special">*</span><span class="identifier">L</span>                               <span class="special">=</span> <span class="number">4</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span>
 168 <span class="identifier">L</span><span class="special">/</span><span class="identifier">L</span>                               <span class="special">=</span> <span class="number">1</span> <span class="identifier">dimensionless</span>
 169 <span class="identifier">L</span><span class="special">*</span><span class="identifier">meter</span>                           <span class="special">=</span> <span class="number">2</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span>
 170 <span class="identifier">kilograms</span><span class="special">*(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">seconds</span><span class="special">)*(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">seconds</span><span class="special">)</span> <span class="special">=</span> <span class="number">4</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span>
 171 <span class="identifier">kilograms</span><span class="special">*(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">seconds</span><span class="special">)^</span><span class="number">2</span>           <span class="special">=</span> <span class="number">4</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span>
 172 <span class="identifier">L</span><span class="special">^</span><span class="number">3</span>                               <span class="special">=</span> <span class="number">8</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span>
 173 <span class="identifier">L</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>                           <span class="special">=</span> <span class="number">2.82843</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>
 174 <span class="number">2</span><span class="identifier">vL</span>                               <span class="special">=</span> <span class="number">1.41421</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>
 175 <span class="special">(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span><span class="identifier">vL</span>                           <span class="special">=</span> <span class="number">1.5874</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">2</span><span class="special">/</span><span class="number">3</span><span class="special">)</span>
 176 </pre>
 177 <p>
 178       </p>
 179 <p>
 180         As a further demonstration of the flexibility of the system, we replace the
 181         <code class="computeroutput"><span class="keyword">double</span></code> value type with a <code class="computeroutput"><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></code> value type (ignoring the question of
 182         the meaningfulness of complex lengths and energies) :
 183       </p>
 184 <p>
 185 </p>
 186 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</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="special">&gt;</span> <span class="identifier">L</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="number">3.0</span><span class="special">,</span><span class="number">4.0</span><span class="special">)*</span><span class="identifier">meters</span><span class="special">);</span>
 187 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">energy</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="special">&gt;</span> <span class="identifier">E</span><span class="special">(</span><span class="identifier">kilograms</span><span class="special">*</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">seconds</span><span class="special">));</span>
 188 </pre>
 189 <p>
 190       </p>
 191 <p>
 192         and find that the code functions exactly as expected with no additional work,
 193         delegating operations to <code class="computeroutput"><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></code> and performing the appropriate dimensional
 194         analysis :
 195       </p>
 196 <p>
 197 </p>
 198 <pre class="programlisting"><span class="identifier">L</span>                                 <span class="special">=</span> <span class="special">(</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)</span> <span class="identifier">m</span>
 199 <span class="identifier">L</span><span class="special">+</span><span class="identifier">L</span>                               <span class="special">=</span> <span class="special">(</span><span class="number">6</span><span class="special">,</span><span class="number">8</span><span class="special">)</span> <span class="identifier">m</span>
 200 <span class="identifier">L</span><span class="special">-</span><span class="identifier">L</span>                               <span class="special">=</span> <span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">)</span> <span class="identifier">m</span>
 201 <span class="identifier">L</span><span class="special">*</span><span class="identifier">L</span>                               <span class="special">=</span> <span class="special">(-</span><span class="number">7</span><span class="special">,</span><span class="number">24</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span>
 202 <span class="identifier">L</span><span class="special">/</span><span class="identifier">L</span>                               <span class="special">=</span> <span class="special">(</span><span class="number">1</span><span class="special">,</span><span class="number">0</span><span class="special">)</span> <span class="identifier">dimensionless</span>
 203 <span class="identifier">L</span><span class="special">*</span><span class="identifier">meter</span>                           <span class="special">=</span> <span class="special">(</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span>
 204 <span class="identifier">kilograms</span><span class="special">*(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">seconds</span><span class="special">)*(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">seconds</span><span class="special">)</span> <span class="special">=</span> <span class="special">(-</span><span class="number">7</span><span class="special">,</span><span class="number">24</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span>
 205 <span class="identifier">kilograms</span><span class="special">*(</span><span class="identifier">L</span><span class="special">/</span><span class="identifier">seconds</span><span class="special">)^</span><span class="number">2</span>           <span class="special">=</span> <span class="special">(-</span><span class="number">7</span><span class="special">,</span><span class="number">24</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span>
 206 <span class="identifier">L</span><span class="special">^</span><span class="number">3</span>                               <span class="special">=</span> <span class="special">(-</span><span class="number">117</span><span class="special">,</span><span class="number">44</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span>
 207 <span class="identifier">L</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>                           <span class="special">=</span> <span class="special">(</span><span class="number">2</span><span class="special">,</span><span class="number">11</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>
 208 <span class="number">2</span><span class="identifier">vL</span>                               <span class="special">=</span> <span class="special">(</span><span class="number">2</span><span class="special">,</span><span class="number">1</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>
 209 <span class="special">(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span><span class="identifier">vL</span>                           <span class="special">=</span> <span class="special">(</span><span class="number">2.38285</span><span class="special">,</span><span class="number">1.69466</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">2</span><span class="special">/</span><span class="number">3</span><span class="special">)</span>
 210 </pre>
 211 <p>
 212       </p>
 213 </div>
 214 <div class="section">
 215 <div class="titlepage"><div><div><h3 class="title">
 216 <a name="boost_units.Examples.KitchenSinkExample"></a><a class="link" href="Examples.html#boost_units.Examples.KitchenSinkExample" title="Kitchen Sink Example using SI units">Kitchen Sink
 217       Example using SI units</a>
 218 </h3></div></div></div>
 219 <div class="toc"><dl class="toc"><dt><span class="section"><a href="Examples.html#boost_units.Examples.KitchenSinkExample.UDT_Quantities">User-defined
 220         value types</a></span></dt></dl></div>
 221 <p>
 222         (<a href="../../../libs/units/example/kitchen_sink.cpp" target="_top">kitchen_sink.cpp</a>)
 223       </p>
 224 <p>
 225         This example provides a fairly extensive set of tests covering most of the
 226         <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
 227         functionality. It uses the SI unit system defined in <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.systems.si_hpp" title="Header &lt;boost/units/systems/si.hpp&gt;">boost/units/systems/si.hpp</a></code>.
 228       </p>
 229 <p>
 230         If we define a few units and associated quantities,
 231       </p>
 232 <p>
 233 </p>
 234 <pre class="programlisting"><span class="comment">/// scalar</span>
 235 <span class="keyword">const</span> <span class="keyword">double</span>    <span class="identifier">s1</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
 236
 237 <span class="keyword">const</span> <span class="keyword">long</span>                  <span class="identifier">x1</span> <span class="special">=</span> <span class="number">2</span><span class="special">;</span>
 238 <span class="keyword">const</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">4</span><span class="special">,</span><span class="number">3</span><span class="special">&gt;</span>  <span class="identifier">x2</span><span class="special">;</span>
 239
 240 <span class="comment">/// define some units</span>
 241 <span class="identifier">force</span>       <span class="identifier">u1</span> <span class="special">=</span> <span class="identifier">newton</span><span class="special">;</span>
 242 <span class="identifier">energy</span>      <span class="identifier">u2</span> <span class="special">=</span> <span class="identifier">joule</span><span class="special">;</span>
 243
 244 <span class="comment">/// define some quantities</span>
 245 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">force</span><span class="special">&gt;</span>      <span class="identifier">q1</span><span class="special">(</span><span class="number">1.0</span><span class="special">*</span><span class="identifier">u1</span><span class="special">);</span>
 246 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">energy</span><span class="special">&gt;</span>     <span class="identifier">q2</span><span class="special">(</span><span class="number">2.0</span><span class="special">*</span><span class="identifier">u2</span><span class="special">);</span>
 247 </pre>
 248 <p>
 249       </p>
 250 <p>
 251         the various algebraic operations between scalars, units, and quantities give
 252       </p>
 253 <p>
 254 </p>
 255 <pre class="programlisting"><span class="identifier">S1</span> <span class="special">:</span>    <span class="number">2</span>
 256 <span class="identifier">X1</span> <span class="special">:</span>    <span class="number">2</span>
 257 <span class="identifier">X2</span> <span class="special">:</span>    <span class="special">(</span><span class="number">4</span><span class="special">/</span><span class="number">3</span><span class="special">)</span>
 258 <span class="identifier">U1</span> <span class="special">:</span>    <span class="identifier">N</span>
 259 <span class="identifier">U2</span> <span class="special">:</span>    <span class="identifier">J</span>
 260 <span class="identifier">Q1</span> <span class="special">:</span>    <span class="number">1</span> <span class="identifier">N</span>
 261 <span class="identifier">Q2</span> <span class="special">:</span>    <span class="number">2</span> <span class="identifier">J</span>
 262 </pre>
 263 <p>
 264       </p>
 265 <p>
 266         Scalar/unit operations :
 267       </p>
 268 <p>
 269 </p>
 270 <pre class="programlisting"><span class="identifier">U1</span><span class="special">*</span><span class="identifier">S1</span> <span class="special">:</span> <span class="number">2</span> <span class="identifier">N</span>
 271 <span class="identifier">S1</span><span class="special">*</span><span class="identifier">U1</span> <span class="special">:</span> <span class="number">2</span> <span class="identifier">N</span>
 272 <span class="identifier">U1</span><span class="special">/</span><span class="identifier">S1</span> <span class="special">:</span> <span class="number">0.5</span> <span class="identifier">N</span>
 273 <span class="identifier">S1</span><span class="special">/</span><span class="identifier">U1</span> <span class="special">:</span> <span class="number">2</span> <span class="identifier">m</span><span class="special">^-</span><span class="number">1</span> <span class="identifier">kg</span><span class="special">^-</span><span class="number">1</span> <span class="identifier">s</span><span class="special">^</span><span class="number">2</span>
 274 </pre>
 275 <p>
 276       </p>
 277 <p>
 278         Unit/unit operations and integral/rational powers of units :
 279       </p>
 280 <p>
 281 </p>
 282 <pre class="programlisting"><span class="identifier">U1</span><span class="special">+</span><span class="identifier">U1</span> <span class="special">:</span> <span class="identifier">N</span>
 283 <span class="identifier">U1</span><span class="special">-</span><span class="identifier">U1</span> <span class="special">:</span> <span class="identifier">N</span>
 284 <span class="identifier">U1</span><span class="special">*</span><span class="identifier">U1</span> <span class="special">:</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span><span class="special">^</span><span class="number">2</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">4</span>
 285 <span class="identifier">U1</span><span class="special">/</span><span class="identifier">U1</span> <span class="special">:</span> <span class="identifier">dimensionless</span>
 286 <span class="identifier">U1</span><span class="special">*</span><span class="identifier">U2</span> <span class="special">:</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span> <span class="identifier">kg</span><span class="special">^</span><span class="number">2</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">4</span>
 287 <span class="identifier">U1</span><span class="special">/</span><span class="identifier">U2</span> <span class="special">:</span> <span class="identifier">m</span><span class="special">^-</span><span class="number">1</span>
 288 <span class="identifier">U1</span><span class="special">^</span><span class="identifier">X</span>  <span class="special">:</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span><span class="special">^</span><span class="number">2</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">4</span>
 289 <span class="identifier">X1vU1</span> <span class="special">:</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">2</span><span class="special">)</span> <span class="identifier">kg</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">2</span><span class="special">)</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">1</span>
 290 <span class="identifier">U1</span><span class="special">^</span><span class="identifier">X2</span> <span class="special">:</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">4</span><span class="special">/</span><span class="number">3</span><span class="special">)</span> <span class="identifier">kg</span><span class="special">^(</span><span class="number">4</span><span class="special">/</span><span class="number">3</span><span class="special">)</span> <span class="identifier">s</span><span class="special">^(-</span><span class="number">8</span><span class="special">/</span><span class="number">3</span><span class="special">)</span>
 291 <span class="identifier">X2vU1</span> <span class="special">:</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">4</span><span class="special">)</span> <span class="identifier">kg</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">4</span><span class="special">)</span> <span class="identifier">s</span><span class="special">^(-</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>
 292 </pre>
 293 <p>
 294       </p>
 295 <p>
 296         Scalar/quantity operations :
 297       </p>
 298 <p>
 299 </p>
 300 <pre class="programlisting"><span class="identifier">Q1</span><span class="special">*</span><span class="identifier">S1</span> <span class="special">:</span> <span class="number">2</span> <span class="identifier">N</span>
 301 <span class="identifier">S1</span><span class="special">*</span><span class="identifier">Q1</span> <span class="special">:</span> <span class="number">2</span> <span class="identifier">N</span>
 302 <span class="identifier">Q1</span><span class="special">/</span><span class="identifier">S1</span> <span class="special">:</span> <span class="number">0.5</span> <span class="identifier">N</span>
 303 <span class="identifier">S1</span><span class="special">/</span><span class="identifier">Q1</span> <span class="special">:</span> <span class="number">2</span> <span class="identifier">m</span><span class="special">^-</span><span class="number">1</span> <span class="identifier">kg</span><span class="special">^-</span><span class="number">1</span> <span class="identifier">s</span><span class="special">^</span><span class="number">2</span>
 304 </pre>
 305 <p>
 306       </p>
 307 <p>
 308         Unit/quantity operations :
 309       </p>
 310 <p>
 311 </p>
 312 <pre class="programlisting"><span class="identifier">U1</span><span class="special">*</span><span class="identifier">Q1</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span><span class="special">^</span><span class="number">2</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">4</span>
 313 <span class="identifier">Q1</span><span class="special">*</span><span class="identifier">U1</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span><span class="special">^</span><span class="number">2</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">4</span>
 314 <span class="identifier">U1</span><span class="special">/</span><span class="identifier">Q1</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">dimensionless</span>
 315 <span class="identifier">Q1</span><span class="special">/</span><span class="identifier">U1</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">dimensionless</span>
 316 </pre>
 317 <p>
 318       </p>
 319 <p>
 320         Quantity/quantity operations and integral/rational powers of quantities :
 321       </p>
 322 <p>
 323 </p>
 324 <pre class="programlisting"><span class="special">+</span><span class="identifier">Q1</span>   <span class="special">:</span> <span class="number">1</span> <span class="identifier">N</span>
 325 <span class="special">-</span><span class="identifier">Q1</span>   <span class="special">:</span> <span class="special">-</span><span class="number">1</span> <span class="identifier">N</span>
 326 <span class="identifier">Q1</span><span class="special">+</span><span class="identifier">Q1</span> <span class="special">:</span> <span class="number">2</span> <span class="identifier">N</span>
 327 <span class="identifier">Q1</span><span class="special">-</span><span class="identifier">Q1</span> <span class="special">:</span> <span class="number">0</span> <span class="identifier">N</span>
 328 <span class="identifier">Q1</span><span class="special">*</span><span class="identifier">Q1</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span><span class="special">^</span><span class="number">2</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">4</span>
 329 <span class="identifier">Q1</span><span class="special">/</span><span class="identifier">Q1</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">dimensionless</span>
 330 <span class="identifier">Q1</span><span class="special">*</span><span class="identifier">Q2</span> <span class="special">:</span> <span class="number">2</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span> <span class="identifier">kg</span><span class="special">^</span><span class="number">2</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">4</span>
 331 <span class="identifier">Q1</span><span class="special">/</span><span class="identifier">Q2</span> <span class="special">:</span> <span class="number">0.5</span> <span class="identifier">m</span><span class="special">^-</span><span class="number">1</span>
 332 <span class="identifier">Q1</span><span class="special">^</span><span class="identifier">X1</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span><span class="special">^</span><span class="number">2</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">4</span>
 333 <span class="identifier">X1vQ1</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">2</span><span class="special">)</span> <span class="identifier">kg</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">2</span><span class="special">)</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">1</span>
 334 <span class="identifier">Q1</span><span class="special">^</span><span class="identifier">X2</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">4</span><span class="special">/</span><span class="number">3</span><span class="special">)</span> <span class="identifier">kg</span><span class="special">^(</span><span class="number">4</span><span class="special">/</span><span class="number">3</span><span class="special">)</span> <span class="identifier">s</span><span class="special">^(-</span><span class="number">8</span><span class="special">/</span><span class="number">3</span><span class="special">)</span>
 335 <span class="identifier">X2vQ1</span> <span class="special">:</span> <span class="number">1</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">4</span><span class="special">)</span> <span class="identifier">kg</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">4</span><span class="special">)</span> <span class="identifier">s</span><span class="special">^(-</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>
 336 </pre>
 337 <p>
 338       </p>
 339 <p>
 340         Logical comparison operators are also defined between quantities :
 341       </p>
 342 <p>
 343 </p>
 344 <pre class="programlisting"><span class="comment">/// check comparison tests</span>
 345 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</span><span class="special">&gt;</span>    <span class="identifier">l1</span><span class="special">(</span><span class="number">1.0</span><span class="special">*</span><span class="identifier">meter</span><span class="special">),</span>
 346                     <span class="identifier">l2</span><span class="special">(</span><span class="number">2.0</span><span class="special">*</span><span class="identifier">meters</span><span class="special">);</span>
 347 </pre>
 348 <p>
 349       </p>
 350 <p>
 351         giving
 352       </p>
 353 <p>
 354 </p>
 355 <pre class="programlisting"><span class="identifier">l1</span> <span class="special">==</span> <span class="identifier">l2</span>    <span class="keyword">false</span>
 356 <span class="identifier">l1</span> <span class="special">!=</span> <span class="identifier">l2</span>    <span class="keyword">true</span>
 357 <span class="identifier">l1</span> <span class="special">&lt;=</span> <span class="identifier">l2</span>    <span class="keyword">true</span>
 358 <span class="identifier">l1</span> <span class="special">&lt;</span> <span class="identifier">l2</span>     <span class="keyword">true</span>
 359 <span class="identifier">l1</span> <span class="special">&gt;=</span> <span class="identifier">l2</span>    <span class="keyword">false</span>
 360 <span class="identifier">l1</span> <span class="special">&gt;</span> <span class="identifier">l2</span>     <span class="keyword">false</span>
 361 </pre>
 362 <p>
 363       </p>
 364 <p>
 365         Implicit conversion is allowed between dimensionless quantities and their
 366         corresponding value types :
 367       </p>
 368 <p>
 369 </p>
 370 <pre class="programlisting"><span class="comment">/// check implicit unit conversion from dimensionless to value_type  </span>
 371 <span class="keyword">const</span> <span class="keyword">double</span>    <span class="identifier">dimless</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">q1</span><span class="special">/</span><span class="identifier">q1</span><span class="special">);</span>
 372 </pre>
 373 <p>
 374       </p>
 375 <p>
 376         A generic function for computing mechanical work can be defined that takes
 377         force and distance arguments in an arbitrary unit system and returns energy
 378         in the same system:
 379       </p>
 380 <p>
 381 </p>
 382 <pre class="programlisting"><span class="comment">/// the physical definition of work - computed for an arbitrary unit system </span>
 383 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">System</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
 384 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">energy_dimension</span><span class="special">,</span><span class="identifier">System</span><span class="special">&gt;,</span><span class="identifier">Y</span><span class="special">&gt;</span>
 385 <span class="identifier">work</span><span class="special">(</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">force_dimension</span><span class="special">,</span><span class="identifier">System</span><span class="special">&gt;,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="identifier">F</span><span class="special">,</span>
 386      <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">System</span><span class="special">&gt;,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="identifier">dx</span><span class="special">)</span>
 387 <span class="special">{</span>
 388     <span class="keyword">return</span> <span class="identifier">F</span><span class="special">*</span><span class="identifier">dx</span><span class="special">;</span>
 389 <span class="special">}</span>
 390 </pre>
 391 <p>
 392       </p>
 393 <p>
 394 </p>
 395 <pre class="programlisting"><span class="comment">/// test calcuation of work</span>
 396 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">force</span><span class="special">&gt;</span>       <span class="identifier">F</span><span class="special">(</span><span class="number">1.0</span><span class="special">*</span><span class="identifier">newton</span><span class="special">);</span>
 397 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</span><span class="special">&gt;</span>      <span class="identifier">dx</span><span class="special">(</span><span class="number">1.0</span><span class="special">*</span><span class="identifier">meter</span><span class="special">);</span>
 398 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">energy</span><span class="special">&gt;</span>      <span class="identifier">E</span><span class="special">(</span><span class="identifier">work</span><span class="special">(</span><span class="identifier">F</span><span class="special">,</span><span class="identifier">dx</span><span class="special">));</span>
 399 </pre>
 400 <p>
 401       </p>
 402 <p>
 403         which functions as expected for SI quantities :
 404       </p>
 405 <p>
 406 </p>
 407 <pre class="programlisting"><span class="identifier">F</span>  <span class="special">=</span> <span class="number">1</span> <span class="identifier">N</span>
 408 <span class="identifier">dx</span> <span class="special">=</span> <span class="number">1</span> <span class="identifier">m</span>
 409 <span class="identifier">E</span>  <span class="special">=</span> <span class="number">1</span> <span class="identifier">J</span>
 410 </pre>
 411 <p>
 412       </p>
 413 <p>
 414         The ideal gas law can also be implemented in SI units :
 415       </p>
 416 <p>
 417 </p>
 418 <pre class="programlisting"><span class="comment">/// the ideal gas law in si units</span>
 419 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
 420 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">amount</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span>
 421 <span class="identifier">idealGasLaw</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">pressure</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">P</span><span class="special">,</span>
 422             <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">volume</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">V</span><span class="special">,</span>
 423             <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">T</span><span class="special">)</span>
 424 <span class="special">{</span>
 425     <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">si</span><span class="special">;</span>
 426
 427     <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">constants</span><span class="special">::</span><span class="identifier">codata</span><span class="special">;</span>
 428     <span class="keyword">return</span> <span class="special">(</span><span class="identifier">P</span><span class="special">*</span><span class="identifier">V</span><span class="special">/(</span><span class="identifier">R</span><span class="special">*</span><span class="identifier">T</span><span class="special">));</span>
 429 <span class="special">}</span>
 430 </pre>
 431 <p>
 432       </p>
 433 <p>
 434 </p>
 435 <pre class="programlisting"><span class="comment">/// test ideal gas law</span>
 436 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">temperature</span><span class="special">&gt;</span>   <span class="identifier">T</span> <span class="special">=</span> <span class="special">(</span><span class="number">273.</span><span class="special">+</span><span class="number">37.</span><span class="special">)*</span><span class="identifier">kelvin</span><span class="special">;</span>
 437 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">pressure</span><span class="special">&gt;</span>      <span class="identifier">P</span> <span class="special">=</span> <span class="number">1.01325e5</span><span class="special">*</span><span class="identifier">pascals</span><span class="special">;</span>
 438 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</span><span class="special">&gt;</span>        <span class="identifier">r</span> <span class="special">=</span> <span class="number">0.5e-6</span><span class="special">*</span><span class="identifier">meters</span><span class="special">;</span>
 439 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">volume</span><span class="special">&gt;</span>        <span class="identifier">V</span> <span class="special">=</span> <span class="special">(</span><span class="number">4.0</span><span class="special">/</span><span class="number">3.0</span><span class="special">)*</span><span class="number">3.141592</span><span class="special">*</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">3</span><span class="special">&gt;(</span><span class="identifier">r</span><span class="special">);</span>
 440 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">amount</span><span class="special">&gt;</span>        <span class="identifier">n</span><span class="special">(</span><span class="identifier">idealGasLaw</span><span class="special">(</span><span class="identifier">P</span><span class="special">,</span><span class="identifier">V</span><span class="special">,</span><span class="identifier">T</span><span class="special">));</span>
 441 </pre>
 442 <p>
 443       </p>
 444 <p>
 445         with the resulting output :
 446       </p>
 447 <p>
 448 </p>
 449 <pre class="programlisting"><span class="identifier">r</span> <span class="special">=</span> <span class="number">5e-07</span> <span class="identifier">m</span>
 450 <span class="identifier">P</span> <span class="special">=</span> <span class="number">101325</span> <span class="identifier">Pa</span>
 451 <span class="identifier">V</span> <span class="special">=</span> <span class="number">5.23599e-19</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span>
 452 <span class="identifier">T</span> <span class="special">=</span> <span class="number">310</span> <span class="identifier">K</span>
 453 <span class="identifier">n</span> <span class="special">=</span> <span class="number">2.05835e-17</span> <span class="identifier">mol</span>
 454 <span class="identifier">R</span> <span class="special">=</span> <span class="number">8.314472</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span> <span class="identifier">K</span><span class="special">^-</span><span class="number">1</span> <span class="identifier">mol</span><span class="special">^-</span><span class="number">1</span> <span class="special">(</span><span class="identifier">rel</span><span class="special">.</span> <span class="identifier">unc</span><span class="special">.</span> <span class="special">=</span> <span class="number">1.8e-06</span><span class="special">)</span>
 455 </pre>
 456 <p>
 457       </p>
 458 <p>
 459         Trigonometric and inverse trigonometric functions can be implemented for
 460         any unit system that provides an angular base dimension. For radians, these
 461         functions are found in <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.cmath_hpp" title="Header &lt;boost/units/cmath.hpp&gt;">boost/units/cmath.hpp</a></code>
 462         These behave as one expects, with trigonometric functions taking an angular
 463         quantity and returning a dimensionless quantity, while the inverse trigonometric
 464         functions take a dimensionless quantity and return an angular quantity :
 465       </p>
 466 <p>
 467         Defining a few angular quantities,
 468       </p>
 469 <p>
 470 </p>
 471 <pre class="programlisting"><span class="comment">/// test trig stuff</span>
 472 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">plane_angle</span><span class="special">&gt;</span>           <span class="identifier">theta</span> <span class="special">=</span> <span class="number">0.375</span><span class="special">*</span><span class="identifier">radians</span><span class="special">;</span>
 473 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">dimensionless</span><span class="special">&gt;</span>         <span class="identifier">sin_theta</span> <span class="special">=</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">theta</span><span class="special">);</span>
 474 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">plane_angle</span><span class="special">&gt;</span>           <span class="identifier">thetap</span> <span class="special">=</span> <span class="identifier">asin</span><span class="special">(</span><span class="identifier">sin_theta</span><span class="special">);</span>
 475 </pre>
 476 <p>
 477       </p>
 478 <p>
 479         yields
 480       </p>
 481 <p>
 482 </p>
 483 <pre class="programlisting"><span class="identifier">theta</span>            <span class="special">=</span> <span class="number">0.375</span> <span class="identifier">rd</span>
 484 <span class="identifier">sin</span><span class="special">(</span><span class="identifier">theta</span><span class="special">)</span>       <span class="special">=</span> <span class="number">0.366273</span> <span class="identifier">dimensionless</span>
 485 <span class="identifier">asin</span><span class="special">(</span><span class="identifier">sin</span><span class="special">(</span><span class="identifier">theta</span><span class="special">))</span> <span class="special">=</span> <span class="number">0.375</span> <span class="identifier">rd</span>
 486 </pre>
 487 <p>
 488       </p>
 489 <p>
 490         Dealing with complex quantities is trivial. Here is the calculation of complex
 491         impedance :
 492       </p>
 493 <p>
 494 </p>
 495 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">electric_potential</span><span class="special">,</span><span class="identifier">complex_type</span><span class="special">&gt;</span> <span class="identifier">v</span> <span class="special">=</span> <span class="identifier">complex_type</span><span class="special">(</span><span class="number">12.5</span><span class="special">,</span><span class="number">0.0</span><span class="special">)*</span><span class="identifier">volts</span><span class="special">;</span>
 496 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">current</span><span class="special">,</span><span class="identifier">complex_type</span><span class="special">&gt;</span>            <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">complex_type</span><span class="special">(</span><span class="number">3.0</span><span class="special">,</span><span class="number">4.0</span><span class="special">)*</span><span class="identifier">amperes</span><span class="special">;</span>
 497 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">resistance</span><span class="special">,</span><span class="identifier">complex_type</span><span class="special">&gt;</span>         <span class="identifier">z</span> <span class="special">=</span> <span class="identifier">complex_type</span><span class="special">(</span><span class="number">1.5</span><span class="special">,-</span><span class="number">2.0</span><span class="special">)*</span><span class="identifier">ohms</span><span class="special">;</span>
 498 </pre>
 499 <p>
 500       </p>
 501 <p>
 502         giving
 503       </p>
 504 <p>
 505 </p>
 506 <pre class="programlisting"><span class="identifier">V</span>   <span class="special">=</span> <span class="special">(</span><span class="number">12.5</span><span class="special">,</span><span class="number">0</span><span class="special">)</span> <span class="identifier">V</span>
 507 <span class="identifier">I</span>   <span class="special">=</span> <span class="special">(</span><span class="number">3</span><span class="special">,</span><span class="number">4</span><span class="special">)</span> <span class="identifier">A</span>
 508 <span class="identifier">Z</span>   <span class="special">=</span> <span class="special">(</span><span class="number">1.5</span><span class="special">,-</span><span class="number">2</span><span class="special">)</span> <span class="identifier">Ohm</span>
 509 <span class="identifier">I</span><span class="special">*</span><span class="identifier">Z</span> <span class="special">=</span> <span class="special">(</span><span class="number">12.5</span><span class="special">,</span><span class="number">0</span><span class="special">)</span> <span class="identifier">V</span>
 510 </pre>
 511 <p>
 512       </p>
 513 <div class="section">
 514 <div class="titlepage"><div><div><h4 class="title">
 515 <a name="boost_units.Examples.KitchenSinkExample.UDT_Quantities"></a><a class="link" href="Examples.html#boost_units.Examples.KitchenSinkExample.UDT_Quantities" title="User-defined value types">User-defined
 516         value types</a>
 517 </h4></div></div></div>
 518 <p>
 519           User-defined value types that support the appropriate arithmetic operations
 520           are automatically supported as quantity value types. The operators that
 521           are supported by default for quantity value types are unary plus, unary
 522           minus, addition, subtraction, multiplication, division, equal-to, not-equal-to,
 523           less-than, less-or-equal-to, greater-than, and greater-or-equal-to. Support
 524           for rational powers and roots can be added by overloading the <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/power_typeof_helper.html" title="Struct template power_typeof_helper">power_typeof_helper</a></code></span>
 525           and <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/root_typeof_helper.html" title="Struct template root_typeof_helper">root_typeof_helper</a></code></span>
 526           classes. Here we implement a user-defined <code class="computeroutput"><span class="identifier">measurement</span></code>
 527           class that models a numerical measurement with an associated measurement
 528           error and the appropriate algebra and demonstrates its use as a quantity
 529           value type; the full code is found in <a href="../../../libs/units/example/measurement.hpp" target="_top">measurement.hpp</a>.
 530         </p>
 531 <p>
 532           Then, defining some <code class="computeroutput"><span class="identifier">measurement</span></code>
 533           <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
 534           variables
 535         </p>
 536 <p>
 537 </p>
 538 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</span><span class="special">,</span><span class="identifier">measurement</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&gt;</span>
 539     <span class="identifier">u</span><span class="special">(</span><span class="identifier">measurement</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="number">1.0</span><span class="special">,</span><span class="number">0.0</span><span class="special">)*</span><span class="identifier">meters</span><span class="special">),</span>
 540     <span class="identifier">w</span><span class="special">(</span><span class="identifier">measurement</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="number">4.52</span><span class="special">,</span><span class="number">0.02</span><span class="special">)*</span><span class="identifier">meters</span><span class="special">),</span>
 541     <span class="identifier">x</span><span class="special">(</span><span class="identifier">measurement</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="number">2.0</span><span class="special">,</span><span class="number">0.2</span><span class="special">)*</span><span class="identifier">meters</span><span class="special">),</span>
 542     <span class="identifier">y</span><span class="special">(</span><span class="identifier">measurement</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="number">3.0</span><span class="special">,</span><span class="number">0.6</span><span class="special">)*</span><span class="identifier">meters</span><span class="special">);</span>
 543 </pre>
 544 <p>
 545         </p>
 546 <p>
 547           gives
 548         </p>
 549 <p>
 550 </p>
 551 <pre class="programlisting"><span class="identifier">x</span><span class="special">+</span><span class="identifier">y</span><span class="special">-</span><span class="identifier">w</span>         <span class="special">=</span> <span class="number">0.48</span><span class="special">(+/-</span><span class="number">0.632772</span><span class="special">)</span> <span class="identifier">m</span>
 552 <span class="identifier">w</span><span class="special">*</span><span class="identifier">x</span>           <span class="special">=</span> <span class="number">9.04</span><span class="special">(+/-</span><span class="number">0.904885</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span>
 553 <span class="identifier">x</span><span class="special">/</span><span class="identifier">y</span>           <span class="special">=</span> <span class="number">0.666667</span><span class="special">(+/-</span><span class="number">0.149071</span><span class="special">)</span> <span class="identifier">dimensionless</span>
 554 </pre>
 555 <p>
 556         </p>
 557 <p>
 558           If we implement the overloaded helper classes for rational powers and roots
 559           then we can also compute rational powers of measurement quantities :
 560         </p>
 561 <p>
 562 </p>
 563 <pre class="programlisting"><span class="identifier">w</span><span class="special">*</span><span class="identifier">y</span><span class="special">^</span><span class="number">2</span><span class="special">/(</span><span class="identifier">u</span><span class="special">*</span><span class="identifier">x</span><span class="special">)^</span><span class="number">2</span> <span class="special">=</span> <span class="number">10.17</span><span class="special">(+/-</span><span class="number">3.52328</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^-</span><span class="number">1</span>
 564 <span class="identifier">w</span><span class="special">/(</span><span class="identifier">u</span><span class="special">*</span><span class="identifier">x</span><span class="special">)^(</span><span class="number">1</span><span class="special">/</span><span class="number">2</span><span class="special">)</span> <span class="special">=</span> <span class="number">3.19612</span><span class="special">(+/-</span><span class="number">0.160431</span><span class="special">)</span> <span class="identifier">dimensionless</span>
 565 </pre>
 566 <p>
 567         </p>
 568 </div>
 569 </div>
 570 <div class="section">
 571 <div class="titlepage"><div><div><h3 class="title">
 572 <a name="boost_units.Examples.ConversionExample"></a><a class="link" href="Examples.html#boost_units.Examples.ConversionExample" title="Conversion Example">Conversion Example</a>
 573 </h3></div></div></div>
 574 <p>
 575         (<a href="../../../libs/units/example/conversion.cpp" target="_top">conversion.cpp</a>)
 576       </p>
 577 <p>
 578         This example demonstrates the various allowed conversions between SI and
 579         CGS units. Defining some quantities
 580       </p>
 581 <p>
 582 </p>
 583 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span>     <span class="identifier">L1</span> <span class="special">=</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">,</span><span class="keyword">int</span><span class="special">&gt;(</span><span class="keyword">int</span><span class="special">(</span><span class="number">2.5</span><span class="special">)*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meters</span><span class="special">);</span>
 584 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">,</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">L2</span><span class="special">(</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">,</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="number">2.5</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meters</span><span class="special">));</span>
 585 </pre>
 586 <p>
 587       </p>
 588 <p>
 589         illustrates implicit conversion of quantities of different value types where
 590         implicit conversion of the value types themselves is allowed. N.B. The conversion
 591         from double to int is treated as an explicit conversion because there is
 592         no way to emulate the exact behavior of the built-in conversion. Explicit
 593         constructors allow conversions for two cases:
 594       </p>
 595 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 596             explicit casting of a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
 597             to a different <code class="computeroutput"><span class="identifier">value_type</span></code>
 598             :
 599           </li></ul></div>
 600 <p>
 601 </p>
 602 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">,</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="identifier">L3</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">,</span><span class="keyword">int</span><span class="special">&gt;</span> <span class="special">&gt;(</span><span class="identifier">L1</span><span class="special">);</span>
 603 </pre>
 604 <p>
 605       </p>
 606 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; "><li class="listitem">
 607             and explicit casting of a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
 608             to a different unit :
 609           </li></ul></div>
 610 <p>
 611 </p>
 612 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span>    <span class="identifier">L4</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="special">&gt;(</span><span class="identifier">L1</span><span class="special">);</span>
 613 </pre>
 614 <p>
 615       </p>
 616 <p>
 617         giving the following output :
 618       </p>
 619 <p>
 620 </p>
 621 <pre class="programlisting"><span class="identifier">L1</span> <span class="special">=</span> <span class="number">2</span> <span class="identifier">m</span>
 622 <span class="identifier">L2</span> <span class="special">=</span> <span class="number">2</span> <span class="identifier">m</span>
 623 <span class="identifier">L3</span> <span class="special">=</span> <span class="number">2</span> <span class="identifier">m</span>
 624 <span class="identifier">L4</span> <span class="special">=</span> <span class="number">200</span> <span class="identifier">cm</span>
 625 <span class="identifier">L5</span> <span class="special">=</span> <span class="number">5</span> <span class="identifier">m</span>
 626 <span class="identifier">L6</span> <span class="special">=</span> <span class="number">4</span> <span class="identifier">m</span>
 627 <span class="identifier">L7</span> <span class="special">=</span> <span class="number">200</span> <span class="identifier">cm</span>
 628 </pre>
 629 <p>
 630       </p>
 631 <p>
 632         A few more explicit unit system conversions :
 633       </p>
 634 <p>
 635 </p>
 636 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">volume</span><span class="special">&gt;</span>    <span class="identifier">vs</span><span class="special">(</span><span class="number">1.0</span><span class="special">*</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">3</span><span class="special">&gt;(</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">));</span>
 637 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">volume</span><span class="special">&gt;</span>   <span class="identifier">vc</span><span class="special">(</span><span class="identifier">vs</span><span class="special">);</span>
 638 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">volume</span><span class="special">&gt;</span>    <span class="identifier">vs2</span><span class="special">(</span><span class="identifier">vc</span><span class="special">);</span>
 639
 640 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">energy</span><span class="special">&gt;</span>    <span class="identifier">es</span><span class="special">(</span><span class="number">1.0</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">joule</span><span class="special">);</span>
 641 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">energy</span><span class="special">&gt;</span>   <span class="identifier">ec</span><span class="special">(</span><span class="identifier">es</span><span class="special">);</span>
 642 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">energy</span><span class="special">&gt;</span>    <span class="identifier">es2</span><span class="special">(</span><span class="identifier">ec</span><span class="special">);</span>
 643
 644 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">velocity</span><span class="special">&gt;</span>  <span class="identifier">v1</span> <span class="special">=</span> <span class="number">2.0</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meters</span><span class="special">/</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span><span class="special">,</span>
 645                         <span class="identifier">v2</span><span class="special">(</span><span class="number">2.0</span><span class="special">*</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">centimeters</span><span class="special">/</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">second</span><span class="special">);</span>
 646 </pre>
 647 <p>
 648       </p>
 649 <p>
 650         which produces the following output:
 651       </p>
 652 <p>
 653 </p>
 654 <pre class="programlisting"><span class="identifier">volume</span> <span class="special">(</span><span class="identifier">m</span><span class="special">^</span><span class="number">3</span><span class="special">)</span>  <span class="special">=</span> <span class="number">1</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span>
 655 <span class="identifier">volume</span> <span class="special">(</span><span class="identifier">cm</span><span class="special">^</span><span class="number">3</span><span class="special">)</span> <span class="special">=</span> <span class="number">1e+06</span> <span class="identifier">cm</span><span class="special">^</span><span class="number">3</span>
 656 <span class="identifier">volume</span> <span class="special">(</span><span class="identifier">m</span><span class="special">^</span><span class="number">3</span><span class="special">)</span>  <span class="special">=</span> <span class="number">1</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span>
 657
 658 <span class="identifier">energy</span> <span class="special">(</span><span class="identifier">joules</span><span class="special">)</span> <span class="special">=</span> <span class="number">1</span> <span class="identifier">J</span>
 659 <span class="identifier">energy</span> <span class="special">(</span><span class="identifier">ergs</span><span class="special">)</span>   <span class="special">=</span> <span class="number">1e+07</span> <span class="identifier">erg</span>
 660 <span class="identifier">energy</span> <span class="special">(</span><span class="identifier">joules</span><span class="special">)</span> <span class="special">=</span> <span class="number">1</span> <span class="identifier">J</span>
 661
 662 <span class="identifier">velocity</span> <span class="special">(</span><span class="number">2</span> <span class="identifier">m</span><span class="special">/</span><span class="identifier">s</span><span class="special">)</span>  <span class="special">=</span> <span class="number">2</span> <span class="identifier">m</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">1</span>
 663 <span class="identifier">velocity</span> <span class="special">(</span><span class="number">2</span> <span class="identifier">cm</span><span class="special">/</span><span class="identifier">s</span><span class="special">)</span> <span class="special">=</span> <span class="number">0.02</span> <span class="identifier">m</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">1</span>
 664 </pre>
 665 <p>
 666       </p>
 667 </div>
 668 <div class="section">
 669 <div class="titlepage"><div><div><h3 class="title">
 670 <a name="boost_units.Examples.UDTExample"></a><a class="link" href="Examples.html#boost_units.Examples.UDTExample" title="User Defined Types">User Defined Types</a>
 671 </h3></div></div></div>
 672 <p>
 673         (<a href="../../../libs/units/example/quaternion.cpp" target="_top">quaternion.cpp</a>)
 674       </p>
 675 <p>
 676         This example demonstrates the use of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span></code>
 677         as a value type for <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
 678         and the converse. For the first case, we first define specializations of
 679         <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/power_typeof_helper.html" title="Struct template power_typeof_helper">power_typeof_helper</a></code></span>
 680         and <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/root_typeof_helper.html" title="Struct template root_typeof_helper">root_typeof_helper</a></code></span>
 681         for powers and roots, respectively:
 682       </p>
 683 <p>
 684 </p>
 685 <pre class="programlisting"><span class="comment">/// specialize power typeof helper</span>
 686 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">N</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">D</span><span class="special">&gt;</span>
 687 <span class="keyword">struct</span> <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;</span>
 688 <span class="special">{</span>
 689     <span class="comment">// boost::math::quaternion only supports integer powers</span>
 690     <span class="identifier">BOOST_STATIC_ASSERT</span><span class="special">(</span><span class="identifier">D</span><span class="special">==</span><span class="number">1</span><span class="special">);</span>
 691
 692     <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span>
 693         <span class="keyword">typename</span> <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span>
 694     <span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span>
 695
 696     <span class="keyword">static</span> <span class="identifier">type</span> <span class="identifier">value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
 697     <span class="special">{</span>
 698         <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;(</span><span class="identifier">N</span><span class="special">));</span>
 699     <span class="special">}</span>
 700 <span class="special">};</span>
 701 </pre>
 702 <p>
 703       </p>
 704 <p>
 705 </p>
 706 <pre class="programlisting"><span class="comment">/// specialize root typeof helper</span>
 707 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">N</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">D</span><span class="special">&gt;</span>
 708 <span class="keyword">struct</span> <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;</span>
 709 <span class="special">{</span>
 710     <span class="comment">// boost::math::quaternion only supports integer powers</span>
 711     <span class="identifier">BOOST_STATIC_ASSERT</span><span class="special">(</span><span class="identifier">N</span><span class="special">==</span><span class="number">1</span><span class="special">);</span>
 712
 713     <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span>
 714         <span class="keyword">typename</span> <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span>
 715     <span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span>
 716
 717     <span class="keyword">static</span> <span class="identifier">type</span> <span class="identifier">value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
 718     <span class="special">{</span>
 719         <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;(</span><span class="identifier">D</span><span class="special">));</span>
 720     <span class="special">}</span>
 721 <span class="special">};</span>
 722 </pre>
 723 <p>
 724       </p>
 725 <p>
 726         We can now declare a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
 727         of a <code class="computeroutput"><span class="identifier">quaternion</span></code> :
 728       </p>
 729 <p>
 730 </p>
 731 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</span><span class="special">,</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&gt;</span>     <span class="identifier">length_dimension</span><span class="special">;</span>
 732
 733 <span class="identifier">length_dimension</span>    <span class="identifier">L</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="number">4.0</span><span class="special">,</span><span class="number">3.0</span><span class="special">,</span><span class="number">2.0</span><span class="special">,</span><span class="number">1.0</span><span class="special">)*</span><span class="identifier">meters</span><span class="special">);</span>
 734 </pre>
 735 <p>
 736       </p>
 737 <p>
 738         so that all operations that are defined in the <code class="computeroutput"><span class="identifier">quaternion</span></code>
 739         class behave correctly. If rational powers were defined for this class, it
 740         would be possible to compute rational powers and roots with no additional
 741         changes.
 742       </p>
 743 <p>
 744 </p>
 745 <pre class="programlisting"><span class="special">+</span><span class="identifier">L</span>      <span class="special">=</span> <span class="special">(</span><span class="number">4</span><span class="special">,</span><span class="number">3</span><span class="special">,</span><span class="number">2</span><span class="special">,</span><span class="number">1</span><span class="special">)</span> <span class="identifier">m</span>
 746 <span class="special">-</span><span class="identifier">L</span>      <span class="special">=</span> <span class="special">(-</span><span class="number">4</span><span class="special">,-</span><span class="number">3</span><span class="special">,-</span><span class="number">2</span><span class="special">,-</span><span class="number">1</span><span class="special">)</span> <span class="identifier">m</span>
 747 <span class="identifier">L</span><span class="special">+</span><span class="identifier">L</span>     <span class="special">=</span> <span class="special">(</span><span class="number">8</span><span class="special">,</span><span class="number">6</span><span class="special">,</span><span class="number">4</span><span class="special">,</span><span class="number">2</span><span class="special">)</span> <span class="identifier">m</span>
 748 <span class="identifier">L</span><span class="special">-</span><span class="identifier">L</span>     <span class="special">=</span> <span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">)</span> <span class="identifier">m</span>
 749 <span class="identifier">L</span><span class="special">*</span><span class="identifier">L</span>     <span class="special">=</span> <span class="special">(</span><span class="number">2</span><span class="special">,</span><span class="number">24</span><span class="special">,</span><span class="number">16</span><span class="special">,</span><span class="number">8</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span>
 750 <span class="identifier">L</span><span class="special">/</span><span class="identifier">L</span>     <span class="special">=</span> <span class="special">(</span><span class="number">1</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">)</span> <span class="identifier">dimensionless</span>
 751 <span class="identifier">L</span><span class="special">^</span><span class="number">3</span>     <span class="special">=</span> <span class="special">(-</span><span class="number">104</span><span class="special">,</span><span class="number">102</span><span class="special">,</span><span class="number">68</span><span class="special">,</span><span class="number">34</span><span class="special">)</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span>
 752 </pre>
 753 <p>
 754       </p>
 755 <p>
 756         Now, if for some reason we preferred the <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span> to be the value
 757         type of the <code class="computeroutput"><span class="identifier">quaternion</span></code> class
 758         we would have :
 759       </p>
 760 <p>
 761 </p>
 762 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="special">&gt;</span>     <span class="identifier">length_dimension</span><span class="special">;</span>
 763
 764 <span class="identifier">length_dimension</span>    <span class="identifier">L</span><span class="special">(</span><span class="number">4.0</span><span class="special">*</span><span class="identifier">meters</span><span class="special">,</span><span class="number">3.0</span><span class="special">*</span><span class="identifier">meters</span><span class="special">,</span><span class="number">2.0</span><span class="special">*</span><span class="identifier">meters</span><span class="special">,</span><span class="number">1.0</span><span class="special">*</span><span class="identifier">meters</span><span class="special">);</span>
 765 </pre>
 766 <p>
 767       </p>
 768 <p>
 769         Here, the unary plus and minus and addition and subtraction operators function
 770         correctly. Unfortunately, the multiplication and division operations fail
 771         because <code class="computeroutput"><span class="identifier">quaternion</span></code> implements
 772         them in terms of the <code class="computeroutput"><span class="special">*=</span></code> and
 773         <code class="computeroutput"><span class="special">/=</span></code> operators, respectively,
 774         which are incapable of representing the heterogeneous unit algebra needed
 775         for quantities (an identical problem occurs with <code class="computeroutput"><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></code>,
 776         for the same reason). In order to compute rational powers and roots, we need
 777         to specialize <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/power_typeof_helper.html" title="Struct template power_typeof_helper">power_typeof_helper</a></code></span>
 778         and <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/root_typeof_helper.html" title="Struct template root_typeof_helper">root_typeof_helper</a></code></span>
 779         as follows:
 780       </p>
 781 <p>
 782 </p>
 783 <pre class="programlisting"><span class="comment">/// specialize power typeof helper for quaternion&lt;quantity&lt;Unit,Y&gt; &gt;</span>
 784 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Unit</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">N</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">D</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
 785 <span class="keyword">struct</span> <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span>
 786     <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="special">&gt;,</span>
 787     <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;</span>
 788 <span class="special">{</span>
 789     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span>
 790         <span class="identifier">Y</span><span class="special">,</span>
 791         <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span>
 792     <span class="special">&gt;::</span><span class="identifier">type</span>     <span class="identifier">value_type</span><span class="special">;</span>
 793
 794     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span>
 795         <span class="identifier">Unit</span><span class="special">,</span>
 796         <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span>
 797     <span class="special">&gt;::</span><span class="identifier">type</span>  <span class="identifier">unit_type</span><span class="special">;</span>
 798
 799     <span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit_type</span><span class="special">,</span><span class="identifier">value_type</span><span class="special">&gt;</span>         <span class="identifier">quantity_type</span><span class="special">;</span>
 800     <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">quantity_type</span><span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span>
 801
 802     <span class="keyword">static</span> <span class="identifier">type</span> <span class="identifier">value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
 803     <span class="special">{</span>
 804         <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">value_type</span><span class="special">&gt;</span>   <span class="identifier">tmp</span> <span class="special">=</span>
 805             <span class="identifier">pow</span><span class="special">&lt;</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;(</span>
 806                 <span class="identifier">x</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">().</span><span class="identifier">value</span><span class="special">(),</span>
 807                 <span class="identifier">x</span><span class="special">.</span><span class="identifier">R_component_2</span><span class="special">().</span><span class="identifier">value</span><span class="special">(),</span>
 808                 <span class="identifier">x</span><span class="special">.</span><span class="identifier">R_component_3</span><span class="special">().</span><span class="identifier">value</span><span class="special">(),</span>
 809                 <span class="identifier">x</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">().</span><span class="identifier">value</span><span class="special">()));</span>
 810
 811         <span class="keyword">return</span> <span class="identifier">type</span><span class="special">(</span><span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">()),</span>
 812                     <span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">R_component_2</span><span class="special">()),</span>
 813                     <span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">R_component_3</span><span class="special">()),</span>
 814                     <span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()));</span>
 815     <span class="special">}</span>
 816 <span class="special">};</span>
 817 </pre>
 818 <p>
 819       </p>
 820 <p>
 821 </p>
 822 <pre class="programlisting"><span class="comment">/// specialize root typeof helper for quaternion&lt;quantity&lt;Unit,Y&gt; &gt;</span>
 823 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Unit</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">N</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">D</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
 824 <span class="keyword">struct</span> <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span>
 825     <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="special">&gt;,</span>
 826     <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;</span>
 827 <span class="special">{</span>
 828     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span>
 829         <span class="identifier">Y</span><span class="special">,</span>
 830         <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span>
 831     <span class="special">&gt;::</span><span class="identifier">type</span>      <span class="identifier">value_type</span><span class="special">;</span>
 832
 833     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span>
 834         <span class="identifier">Unit</span><span class="special">,</span>
 835         <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span>
 836     <span class="special">&gt;::</span><span class="identifier">type</span>   <span class="identifier">unit_type</span><span class="special">;</span>
 837
 838     <span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit_type</span><span class="special">,</span><span class="identifier">value_type</span><span class="special">&gt;</span>         <span class="identifier">quantity_type</span><span class="special">;</span>
 839     <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">quantity_type</span><span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span>
 840
 841     <span class="keyword">static</span> <span class="identifier">type</span> <span class="identifier">value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
 842     <span class="special">{</span>
 843         <span class="keyword">const</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">value_type</span><span class="special">&gt;</span>   <span class="identifier">tmp</span> <span class="special">=</span>
 844             <span class="identifier">root</span><span class="special">&lt;</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;(</span>
 845                 <span class="identifier">x</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">().</span><span class="identifier">value</span><span class="special">(),</span>
 846                 <span class="identifier">x</span><span class="special">.</span><span class="identifier">R_component_2</span><span class="special">().</span><span class="identifier">value</span><span class="special">(),</span>
 847                 <span class="identifier">x</span><span class="special">.</span><span class="identifier">R_component_3</span><span class="special">().</span><span class="identifier">value</span><span class="special">(),</span>
 848                 <span class="identifier">x</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">().</span><span class="identifier">value</span><span class="special">()));</span>
 849
 850         <span class="keyword">return</span> <span class="identifier">type</span><span class="special">(</span><span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">()),</span>
 851                     <span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">R_component_2</span><span class="special">()),</span>
 852                     <span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">R_component_3</span><span class="special">()),</span>
 853                     <span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()));</span>
 854     <span class="special">}</span>
 855 <span class="special">};</span>
 856 </pre>
 857 <p>
 858       </p>
 859 <p>
 860         giving:
 861       </p>
 862 <p>
 863 </p>
 864 <pre class="programlisting"><span class="special">+</span><span class="identifier">L</span>      <span class="special">=</span> <span class="special">(</span><span class="number">4</span> <span class="identifier">m</span><span class="special">,</span><span class="number">3</span> <span class="identifier">m</span><span class="special">,</span><span class="number">2</span> <span class="identifier">m</span><span class="special">,</span><span class="number">1</span> <span class="identifier">m</span><span class="special">)</span>
 865 <span class="special">-</span><span class="identifier">L</span>      <span class="special">=</span> <span class="special">(-</span><span class="number">4</span> <span class="identifier">m</span><span class="special">,-</span><span class="number">3</span> <span class="identifier">m</span><span class="special">,-</span><span class="number">2</span> <span class="identifier">m</span><span class="special">,-</span><span class="number">1</span> <span class="identifier">m</span><span class="special">)</span>
 866 <span class="identifier">L</span><span class="special">+</span><span class="identifier">L</span>     <span class="special">=</span> <span class="special">(</span><span class="number">8</span> <span class="identifier">m</span><span class="special">,</span><span class="number">6</span> <span class="identifier">m</span><span class="special">,</span><span class="number">4</span> <span class="identifier">m</span><span class="special">,</span><span class="number">2</span> <span class="identifier">m</span><span class="special">)</span>
 867 <span class="identifier">L</span><span class="special">-</span><span class="identifier">L</span>     <span class="special">=</span> <span class="special">(</span><span class="number">0</span> <span class="identifier">m</span><span class="special">,</span><span class="number">0</span> <span class="identifier">m</span><span class="special">,</span><span class="number">0</span> <span class="identifier">m</span><span class="special">,</span><span class="number">0</span> <span class="identifier">m</span><span class="special">)</span>
 868 <span class="identifier">L</span><span class="special">^</span><span class="number">3</span>     <span class="special">=</span> <span class="special">(-</span><span class="number">104</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span><span class="special">,</span><span class="number">102</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span><span class="special">,</span><span class="number">68</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span><span class="special">,</span><span class="number">34</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span><span class="special">)</span>
 869 </pre>
 870 <p>
 871       </p>
 872 </div>
 873 <div class="section">
 874 <div class="titlepage"><div><div><h3 class="title">
 875 <a name="boost_units.Examples.ComplexExample"></a><a class="link" href="Examples.html#boost_units.Examples.ComplexExample" title="Complex Example">Complex Example</a>
 876 </h3></div></div></div>
 877 <p>
 878         (<a href="../../../libs/units/example/complex.cpp" target="_top">complex.cpp</a>)
 879       </p>
 880 <p>
 881         This example demonstrates how to implement a replacement <code class="computeroutput"><span class="identifier">complex</span></code>
 882         class that functions correctly both as a quantity value type and as a quantity
 883         container class, including heterogeneous multiplication and division operations
 884         and rational powers and roots. Naturally, heterogeneous operations are only
 885         supported on compilers that implement <code class="computeroutput"><span class="identifier">typeof</span></code>.
 886         The primary differences are that binary operations are not implemented using
 887         the <code class="computeroutput"><span class="identifier">op</span><span class="special">=</span></code>
 888         operators and use the utility classes <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/add_typeof_helper.html" title="Struct template add_typeof_helper">add_typeof_helper</a></code></span>,
 889         <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/subtract_typeof_helper.html" title="Struct template subtract_typeof_helper">subtract_typeof_helper</a></code></span>,
 890         <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/multiply_typeof_helper.html" title="Struct template multiply_typeof_helper">multiply_typeof_helper</a></code></span>,
 891         and <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/divide_typeof_helper.html" title="Struct template divide_typeof_helper">divide_typeof_helper</a></code></span>.
 892         In addition, <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/power_typeof_helper.html" title="Struct template power_typeof_helper">power_typeof_helper</a></code></span>
 893         and <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/root_typeof_helper.html" title="Struct template root_typeof_helper">root_typeof_helper</a></code></span>
 894         are defined for both cases :
 895       </p>
 896 <p>
 897 </p>
 898 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
 899
 900 <span class="keyword">namespace</span> <span class="identifier">units</span> <span class="special">{</span>
 901
 902 <span class="comment">/// replacement complex class </span>
 903 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">T</span><span class="special">&gt;</span>
 904 <span class="keyword">class</span> <span class="identifier">complex</span>
 905 <span class="special">{</span>
 906     <span class="keyword">public</span><span class="special">:</span>
 907         <span class="keyword">typedef</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span>  <span class="identifier">this_type</span><span class="special">;</span>
 908
 909         <span class="identifier">complex</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">r</span> <span class="special">=</span> <span class="number">0</span><span class="special">,</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">r_</span><span class="special">(</span><span class="identifier">r</span><span class="special">),</span><span class="identifier">i_</span><span class="special">(</span><span class="identifier">i</span><span class="special">)</span> <span class="special">{</span> <span class="special">}</span>
 910         <span class="identifier">complex</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="identifier">source</span><span class="special">)</span> <span class="special">:</span> <span class="identifier">r_</span><span class="special">(</span><span class="identifier">source</span><span class="special">.</span><span class="identifier">r_</span><span class="special">),</span><span class="identifier">i_</span><span class="special">(</span><span class="identifier">source</span><span class="special">.</span><span class="identifier">i_</span><span class="special">)</span> <span class="special">{</span> <span class="special">}</span>
 911
 912         <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">=(</span><span class="keyword">const</span> <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="identifier">source</span><span class="special">)</span>
 913         <span class="special">{</span>
 914             <span class="keyword">if</span> <span class="special">(</span><span class="keyword">this</span> <span class="special">==</span> <span class="special">&amp;</span><span class="identifier">source</span><span class="special">)</span> <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 915
 916             <span class="identifier">r_</span> <span class="special">=</span> <span class="identifier">source</span><span class="special">.</span><span class="identifier">r_</span><span class="special">;</span>
 917             <span class="identifier">i_</span> <span class="special">=</span> <span class="identifier">source</span><span class="special">.</span><span class="identifier">i_</span><span class="special">;</span>
 918
 919             <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 920         <span class="special">}</span>
 921
 922         <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">real</span><span class="special">()</span>                   <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">r_</span><span class="special">;</span> <span class="special">}</span>
 923         <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">imag</span><span class="special">()</span>                   <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">i_</span><span class="special">;</span> <span class="special">}</span>
 924
 925         <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">real</span><span class="special">()</span> <span class="keyword">const</span>       <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">r_</span><span class="special">;</span> <span class="special">}</span>
 926         <span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">imag</span><span class="special">()</span> <span class="keyword">const</span>       <span class="special">{</span> <span class="keyword">return</span> <span class="identifier">i_</span><span class="special">;</span> <span class="special">}</span>
 927
 928         <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 929         <span class="special">{</span>
 930             <span class="identifier">r_</span> <span class="special">+=</span> <span class="identifier">val</span><span class="special">;</span>
 931             <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 932         <span class="special">}</span>
 933
 934         <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">-=(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 935         <span class="special">{</span>
 936             <span class="identifier">r_</span> <span class="special">-=</span> <span class="identifier">val</span><span class="special">;</span>
 937             <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 938         <span class="special">}</span>
 939
 940         <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">*=(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 941         <span class="special">{</span>
 942             <span class="identifier">r_</span> <span class="special">*=</span> <span class="identifier">val</span><span class="special">;</span>
 943             <span class="identifier">i_</span> <span class="special">*=</span> <span class="identifier">val</span><span class="special">;</span>
 944             <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 945         <span class="special">}</span>
 946
 947         <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">/=(</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">val</span><span class="special">)</span>
 948         <span class="special">{</span>
 949             <span class="identifier">r_</span> <span class="special">/=</span> <span class="identifier">val</span><span class="special">;</span>
 950             <span class="identifier">i_</span> <span class="special">/=</span> <span class="identifier">val</span><span class="special">;</span>
 951             <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 952         <span class="special">}</span>
 953
 954         <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">+=(</span><span class="keyword">const</span> <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="identifier">source</span><span class="special">)</span>
 955         <span class="special">{</span>
 956             <span class="identifier">r_</span> <span class="special">+=</span> <span class="identifier">source</span><span class="special">.</span><span class="identifier">r_</span><span class="special">;</span>
 957             <span class="identifier">i_</span> <span class="special">+=</span> <span class="identifier">source</span><span class="special">.</span><span class="identifier">i_</span><span class="special">;</span>
 958             <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 959         <span class="special">}</span>
 960
 961         <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">-=(</span><span class="keyword">const</span> <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="identifier">source</span><span class="special">)</span>
 962         <span class="special">{</span>
 963             <span class="identifier">r_</span> <span class="special">-=</span> <span class="identifier">source</span><span class="special">.</span><span class="identifier">r_</span><span class="special">;</span>
 964             <span class="identifier">i_</span> <span class="special">-=</span> <span class="identifier">source</span><span class="special">.</span><span class="identifier">i_</span><span class="special">;</span>
 965             <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 966         <span class="special">}</span>
 967
 968         <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">*=(</span><span class="keyword">const</span> <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="identifier">source</span><span class="special">)</span>
 969         <span class="special">{</span>
 970             <span class="special">*</span><span class="keyword">this</span> <span class="special">=</span> <span class="special">*</span><span class="keyword">this</span> <span class="special">*</span> <span class="identifier">source</span><span class="special">;</span>
 971             <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 972         <span class="special">}</span>
 973
 974         <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">/=(</span><span class="keyword">const</span> <span class="identifier">this_type</span><span class="special">&amp;</span> <span class="identifier">source</span><span class="special">)</span>
 975         <span class="special">{</span>
 976             <span class="special">*</span><span class="keyword">this</span> <span class="special">=</span> <span class="special">*</span><span class="keyword">this</span> <span class="special">/</span> <span class="identifier">source</span><span class="special">;</span>
 977             <span class="keyword">return</span> <span class="special">*</span><span class="keyword">this</span><span class="special">;</span>
 978         <span class="special">}</span>
 979
 980     <span class="keyword">private</span><span class="special">:</span>
 981         <span class="identifier">T</span>   <span class="identifier">r_</span><span class="special">,</span><span class="identifier">i_</span><span class="special">;</span>
 982 <span class="special">};</span>
 983
 984 <span class="special">}</span>
 985
 986 <span class="special">}</span>
 987
 988 <span class="preprocessor">#if</span> <span class="identifier">BOOST_UNITS_HAS_BOOST_TYPEOF</span>
 989
 990 <span class="preprocessor">#include</span> <span class="identifier">BOOST_TYPEOF_INCREMENT_REGISTRATION_GROUP</span><span class="special">()</span>
 991
 992 <span class="identifier">BOOST_TYPEOF_REGISTER_TEMPLATE</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">complex</span><span class="special">,</span> <span class="number">1</span><span class="special">)</span>
 993
 994 <span class="preprocessor">#endif</span>
 995
 996 <span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span>
 997
 998 <span class="keyword">namespace</span> <span class="identifier">units</span> <span class="special">{</span>
 999
1000 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">X</span><span class="special">&gt;</span>
1001 <span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">unary_plus_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span>
1002 <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
1003 <span class="special">{</span>
1004     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">unary_plus_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;::</span><span class="identifier">type</span>  <span class="identifier">type</span><span class="special">;</span>
1005
1006     <span class="keyword">return</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">type</span><span class="special">&gt;(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">(),</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">());</span>
1007 <span class="special">}</span>
1008
1009 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">X</span><span class="special">&gt;</span>
1010 <span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">unary_minus_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span>
1011 <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
1012 <span class="special">{</span>
1013     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">unary_minus_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">type</span><span class="special">;</span>
1014
1015     <span class="keyword">return</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">type</span><span class="special">&gt;(-</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">(),-</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">());</span>
1016 <span class="special">}</span>
1017
1018 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">X</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
1019 <span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">add_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span>
1020 <span class="keyword">operator</span><span class="special">+(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">,</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">y</span><span class="special">)</span>
1021 <span class="special">{</span>
1022     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">add_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">type</span><span class="special">;</span>
1023
1024     <span class="keyword">return</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">type</span><span class="special">&gt;(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">()+</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">(),</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()+</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">());</span>
1025 <span class="special">}</span>
1026
1027 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">X</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
1028 <span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">subtract_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span>
1029 <span class="keyword">operator</span><span class="special">-(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">,</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">y</span><span class="special">)</span>
1030 <span class="special">{</span>
1031     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">subtract_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;::</span><span class="identifier">type</span>    <span class="identifier">type</span><span class="special">;</span>
1032
1033     <span class="keyword">return</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">type</span><span class="special">&gt;(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">()-</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">(),</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()-</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">());</span>
1034 <span class="special">}</span>
1035
1036 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">X</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
1037 <span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">multiply_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span>
1038 <span class="keyword">operator</span><span class="special">*(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">,</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">y</span><span class="special">)</span>
1039 <span class="special">{</span>
1040     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">multiply_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;::</span><span class="identifier">type</span>    <span class="identifier">type</span><span class="special">;</span>
1041
1042     <span class="keyword">return</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">type</span><span class="special">&gt;(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span> <span class="special">-</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">(),</span>
1043                          <span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()</span> <span class="special">+</span> <span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">());</span>
1044
1045 <span class="comment">//  fully correct implementation has more complex return type</span>
1046 <span class="comment">//</span>
1047 <span class="comment">//    typedef typename boost::units::multiply_typeof_helper&lt;X,Y&gt;::type xy_type;</span>
1048 <span class="comment">//    </span>
1049 <span class="comment">//    typedef typename boost::units::add_typeof_helper&lt;</span>
1050 <span class="comment">//      xy_type,xy_type&gt;::type         xy_plus_xy_type;</span>
1051 <span class="comment">//    typedef typename</span>
1052 <span class="comment">//        boost::units::subtract_typeof_helper&lt;xy_type,xy_type&gt;::type</span>
1053 <span class="comment">//        xy_minus_xy_type;</span>
1054 <span class="comment">//    </span>
1055 <span class="comment">//    BOOST_STATIC_ASSERT((boost::is_same&lt;xy_plus_xy_type,</span>
1056 <span class="comment">//                                       xy_minus_xy_type&gt;::value == true));</span>
1057 <span class="comment">//    </span>
1058 <span class="comment">//    return complex&lt;xy_plus_xy_type&gt;(x.real()*y.real()-x.imag()*y.imag(),</span>
1059 <span class="comment">//                                    x.real()*y.imag()+x.imag()*y.real());</span>
1060 <span class="special">}</span>
1061
1062 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">X</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
1063 <span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">divide_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;::</span><span class="identifier">type</span><span class="special">&gt;</span>
1064 <span class="keyword">operator</span><span class="special">/(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">,</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">y</span><span class="special">)</span>
1065 <span class="special">{</span>
1066     <span class="comment">// naive implementation of complex division</span>
1067     <span class="keyword">typedef</span> <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">divide_typeof_helper</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">type</span><span class="special">;</span>
1068
1069     <span class="keyword">return</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">type</span><span class="special">&gt;((</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">()+</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">())/</span>
1070                             <span class="special">(</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">()+</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()),</span>
1071                          <span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">()-</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">())/</span>
1072                             <span class="special">(</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">real</span><span class="special">()+</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()*</span><span class="identifier">y</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()));</span>
1073
1074 <span class="comment">//  fully correct implementation has more complex return type</span>
1075 <span class="comment">//</span>
1076 <span class="comment">//  typedef typename boost::units::multiply_typeof_helper&lt;X,Y&gt;::type xy_type;</span>
1077 <span class="comment">//  typedef typename boost::units::multiply_typeof_helper&lt;Y,Y&gt;::type yy_type;</span>
1078 <span class="comment">//</span>
1079 <span class="comment">//  typedef typename boost::units::add_typeof_helper&lt;xy_type, xy_type&gt;::type</span>
1080 <span class="comment">//      xy_plus_xy_type;</span>
1081 <span class="comment">//  typedef typename boost::units::subtract_typeof_helper&lt;</span>
1082 <span class="comment">//      xy_type,xy_type&gt;::type xy_minus_xy_type;</span>
1083 <span class="comment">//</span>
1084 <span class="comment">//  typedef typename boost::units::divide_typeof_helper&lt;</span>
1085 <span class="comment">//      xy_plus_xy_type,yy_type&gt;::type      xy_plus_xy_over_yy_type;</span>
1086 <span class="comment">//  typedef typename boost::units::divide_typeof_helper&lt;</span>
1087 <span class="comment">//      xy_minus_xy_type,yy_type&gt;::type     xy_minus_xy_over_yy_type;</span>
1088 <span class="comment">//</span>
1089 <span class="comment">//  BOOST_STATIC_ASSERT((boost::is_same&lt;xy_plus_xy_over_yy_type,</span>
1090 <span class="comment">//                                  xy_minus_xy_over_yy_type&gt;::value == true));</span>
1091 <span class="comment">//</span>
1092 <span class="comment">//  return complex&lt;xy_plus_xy_over_yy_type&gt;(</span>
1093 <span class="comment">//      (x.real()*y.real()+x.imag()*y.imag())/</span>
1094 <span class="comment">//          (y.real()*y.real()+y.imag()*y.imag()),</span>
1095 <span class="comment">//      (x.imag()*y.real()-x.real()*y.imag())/</span>
1096 <span class="comment">//          (y.real()*y.real()+y.imag()*y.imag()));</span>
1097 <span class="special">}</span>
1098
1099 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
1100 <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;</span>
1101 <span class="identifier">pow</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">,</span><span class="keyword">const</span> <span class="identifier">Y</span><span class="special">&amp;</span> <span class="identifier">y</span><span class="special">)</span>
1102 <span class="special">{</span>
1103     <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="identifier">tmp</span><span class="special">(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">(),</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">());</span>
1104
1105     <span class="identifier">tmp</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">,</span><span class="identifier">y</span><span class="special">);</span>
1106
1107     <span class="keyword">return</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">real</span><span class="special">(),</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">imag</span><span class="special">());</span>
1108 <span class="special">}</span>
1109
1110 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">&gt;</span>
1111 <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&amp;</span> <span class="keyword">operator</span><span class="special">&lt;&lt;(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">val</span><span class="special">)</span>
1112 <span class="special">{</span>
1113     <span class="identifier">os</span> <span class="special">&lt;&lt;</span> <span class="identifier">val</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" + "</span> <span class="special">&lt;&lt;</span> <span class="identifier">val</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()</span> <span class="special">&lt;&lt;</span> <span class="string">" i"</span><span class="special">;</span>
1114
1115     <span class="keyword">return</span> <span class="identifier">os</span><span class="special">;</span>
1116 <span class="special">}</span>
1117
1118 <span class="comment">/// specialize power typeof helper for complex&lt;Y&gt;</span>
1119 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">N</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">D</span><span class="special">&gt;</span>
1120 <span class="keyword">struct</span> <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;</span>
1121 <span class="special">{</span>
1122     <span class="keyword">typedef</span> <span class="identifier">complex</span><span class="special">&lt;</span>
1123         <span class="keyword">typename</span> <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span>
1124     <span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span>
1125
1126     <span class="keyword">static</span> <span class="identifier">type</span> <span class="identifier">value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
1127     <span class="special">{</span>
1128         <span class="keyword">const</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span>  <span class="identifier">rat</span><span class="special">;</span>
1129
1130         <span class="keyword">const</span> <span class="identifier">Y</span>    <span class="identifier">m</span> <span class="special">=</span> <span class="identifier">Y</span><span class="special">(</span><span class="identifier">rat</span><span class="special">.</span><span class="identifier">numerator</span><span class="special">())/</span><span class="identifier">Y</span><span class="special">(</span><span class="identifier">rat</span><span class="special">.</span><span class="identifier">denominator</span><span class="special">());</span>
1131
1132         <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">m</span><span class="special">);</span>
1133     <span class="special">}</span>
1134 <span class="special">};</span>
1135
1136 <span class="comment">/// specialize root typeof helper for complex&lt;Y&gt;</span>
1137 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">N</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">D</span><span class="special">&gt;</span>
1138 <span class="keyword">struct</span> <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;</span>
1139 <span class="special">{</span>
1140     <span class="keyword">typedef</span> <span class="identifier">complex</span><span class="special">&lt;</span>
1141         <span class="keyword">typename</span> <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span>
1142     <span class="special">&gt;</span> <span class="identifier">type</span><span class="special">;</span>
1143
1144     <span class="keyword">static</span> <span class="identifier">type</span> <span class="identifier">value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
1145     <span class="special">{</span>
1146         <span class="keyword">const</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span>  <span class="identifier">rat</span><span class="special">;</span>
1147
1148         <span class="keyword">const</span> <span class="identifier">Y</span>    <span class="identifier">m</span> <span class="special">=</span> <span class="identifier">Y</span><span class="special">(</span><span class="identifier">rat</span><span class="special">.</span><span class="identifier">denominator</span><span class="special">())/</span><span class="identifier">Y</span><span class="special">(</span><span class="identifier">rat</span><span class="special">.</span><span class="identifier">numerator</span><span class="special">());</span>
1149
1150         <span class="keyword">return</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">pow</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span><span class="identifier">m</span><span class="special">);</span>
1151     <span class="special">}</span>
1152 <span class="special">};</span>
1153
1154 <span class="comment">/// specialize power typeof helper for complex&lt;quantity&lt;Unit,Y&gt; &gt;</span>
1155 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Unit</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">N</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">D</span><span class="special">&gt;</span>
1156 <span class="keyword">struct</span> <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="special">&gt;,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;</span>
1157 <span class="special">{</span>
1158     <span class="keyword">typedef</span> <span class="keyword">typename</span>
1159         <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span>       <span class="identifier">value_type</span><span class="special">;</span>
1160     <span class="keyword">typedef</span> <span class="keyword">typename</span>
1161         <span class="identifier">power_typeof_helper</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span>    <span class="identifier">unit_type</span><span class="special">;</span>
1162     <span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit_type</span><span class="special">,</span><span class="identifier">value_type</span><span class="special">&gt;</span>                      <span class="identifier">quantity_type</span><span class="special">;</span>
1163     <span class="keyword">typedef</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">quantity_type</span><span class="special">&gt;</span>                              <span class="identifier">type</span><span class="special">;</span>
1164
1165     <span class="keyword">static</span> <span class="identifier">type</span> <span class="identifier">value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
1166     <span class="special">{</span>
1167         <span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">value_type</span><span class="special">&gt;</span>   <span class="identifier">tmp</span> <span class="special">=</span>
1168             <span class="identifier">pow</span><span class="special">&lt;</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;(</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">().</span><span class="identifier">value</span><span class="special">(),</span>
1169                                                   <span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">().</span><span class="identifier">value</span><span class="special">()));</span>
1170
1171         <span class="keyword">return</span> <span class="identifier">type</span><span class="special">(</span><span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">real</span><span class="special">()),</span>
1172                     <span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()));</span>
1173     <span class="special">}</span>
1174 <span class="special">};</span>
1175
1176 <span class="comment">/// specialize root typeof helper for complex&lt;quantity&lt;Unit,Y&gt; &gt;</span>
1177 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Y</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">Unit</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">N</span><span class="special">,</span><span class="keyword">long</span> <span class="identifier">D</span><span class="special">&gt;</span>
1178 <span class="keyword">struct</span> <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="special">&gt;,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;</span>
1179 <span class="special">{</span>
1180     <span class="keyword">typedef</span> <span class="keyword">typename</span>
1181         <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span>       <span class="identifier">value_type</span><span class="special">;</span>
1182     <span class="keyword">typedef</span> <span class="keyword">typename</span>
1183         <span class="identifier">root_typeof_helper</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span>    <span class="identifier">unit_type</span><span class="special">;</span>
1184     <span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit_type</span><span class="special">,</span><span class="identifier">value_type</span><span class="special">&gt;</span>                      <span class="identifier">quantity_type</span><span class="special">;</span>
1185     <span class="keyword">typedef</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">quantity_type</span><span class="special">&gt;</span>                              <span class="identifier">type</span><span class="special">;</span>
1186
1187     <span class="keyword">static</span> <span class="identifier">type</span> <span class="identifier">value</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">Unit</span><span class="special">,</span><span class="identifier">Y</span><span class="special">&gt;</span> <span class="special">&gt;&amp;</span> <span class="identifier">x</span><span class="special">)</span>
1188     <span class="special">{</span>
1189         <span class="keyword">const</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">value_type</span><span class="special">&gt;</span>   <span class="identifier">tmp</span> <span class="special">=</span>
1190             <span class="identifier">root</span><span class="special">&lt;</span><span class="identifier">static_rational</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">,</span><span class="identifier">D</span><span class="special">&gt;</span> <span class="special">&gt;(</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">Y</span><span class="special">&gt;(</span><span class="identifier">x</span><span class="special">.</span><span class="identifier">real</span><span class="special">().</span><span class="identifier">value</span><span class="special">(),</span>
1191                                                    <span class="identifier">x</span><span class="special">.</span><span class="identifier">imag</span><span class="special">().</span><span class="identifier">value</span><span class="special">()));</span>
1192
1193         <span class="keyword">return</span> <span class="identifier">type</span><span class="special">(</span><span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">real</span><span class="special">()),</span>
1194                    <span class="identifier">quantity_type</span><span class="special">::</span><span class="identifier">from_value</span><span class="special">(</span><span class="identifier">tmp</span><span class="special">.</span><span class="identifier">imag</span><span class="special">()));</span>
1195     <span class="special">}</span>
1196 <span class="special">};</span>
1197
1198 <span class="special">}</span> <span class="comment">// namespace units</span>
1199
1200 <span class="special">}</span> <span class="comment">// namespace boost</span>
1201 </pre>
1202 <p>
1203       </p>
1204 <p>
1205         With this replacement <code class="computeroutput"><span class="identifier">complex</span></code>
1206         class, we can declare a complex variable :
1207       </p>
1208 <p>
1209 </p>
1210 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</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="special">&gt;</span>     <span class="identifier">length_dimension</span><span class="special">;</span>
1211
1212 <span class="identifier">length_dimension</span>    <span class="identifier">L</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="number">2.0</span><span class="special">,</span><span class="number">1.0</span><span class="special">)*</span><span class="identifier">meters</span><span class="special">);</span>
1213 </pre>
1214 <p>
1215       </p>
1216 <p>
1217         to get the correct behavior for all cases supported by <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span> with a <code class="computeroutput"><span class="identifier">complex</span></code> value type :
1218       </p>
1219 <p>
1220 </p>
1221 <pre class="programlisting"><span class="special">+</span><span class="identifier">L</span>      <span class="special">=</span> <span class="number">2</span> <span class="special">+</span> <span class="number">1</span> <span class="identifier">i</span> <span class="identifier">m</span>
1222 <span class="special">-</span><span class="identifier">L</span>      <span class="special">=</span> <span class="special">-</span><span class="number">2</span> <span class="special">+</span> <span class="special">-</span><span class="number">1</span> <span class="identifier">i</span> <span class="identifier">m</span>
1223 <span class="identifier">L</span><span class="special">+</span><span class="identifier">L</span>     <span class="special">=</span> <span class="number">4</span> <span class="special">+</span> <span class="number">2</span> <span class="identifier">i</span> <span class="identifier">m</span>
1224 <span class="identifier">L</span><span class="special">-</span><span class="identifier">L</span>     <span class="special">=</span> <span class="number">0</span> <span class="special">+</span> <span class="number">0</span> <span class="identifier">i</span> <span class="identifier">m</span>
1225 <span class="identifier">L</span><span class="special">*</span><span class="identifier">L</span>     <span class="special">=</span> <span class="number">3</span> <span class="special">+</span> <span class="number">4</span> <span class="identifier">i</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span>
1226 <span class="identifier">L</span><span class="special">/</span><span class="identifier">L</span>     <span class="special">=</span> <span class="number">1</span> <span class="special">+</span> <span class="number">0</span> <span class="identifier">i</span> <span class="identifier">dimensionless</span>
1227 <span class="identifier">L</span><span class="special">^</span><span class="number">3</span>     <span class="special">=</span> <span class="number">2</span> <span class="special">+</span> <span class="number">11</span> <span class="identifier">i</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span>
1228 <span class="identifier">L</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span> <span class="special">=</span> <span class="number">2.56713</span> <span class="special">+</span> <span class="number">2.14247</span> <span class="identifier">i</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span>
1229 <span class="number">3</span><span class="identifier">vL</span>     <span class="special">=</span> <span class="number">1.29207</span> <span class="special">+</span> <span class="number">0.201294</span> <span class="identifier">i</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">3</span><span class="special">)</span>
1230 <span class="special">(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span><span class="identifier">vL</span> <span class="special">=</span> <span class="number">1.62894</span> <span class="special">+</span> <span class="number">0.520175</span> <span class="identifier">i</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">2</span><span class="special">/</span><span class="number">3</span><span class="special">)</span>
1231 </pre>
1232 <p>
1233       </p>
1234 <p>
1235         and, similarly, <code class="computeroutput"><span class="identifier">complex</span></code> with
1236         a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
1237         value type
1238       </p>
1239 <p>
1240 </p>
1241 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="special">&gt;</span>     <span class="identifier">length_dimension</span><span class="special">;</span>
1242
1243 <span class="identifier">length_dimension</span>    <span class="identifier">L</span><span class="special">(</span><span class="number">2.0</span><span class="special">*</span><span class="identifier">meters</span><span class="special">,</span><span class="number">1.0</span><span class="special">*</span><span class="identifier">meters</span><span class="special">);</span>
1244 </pre>
1245 <p>
1246       </p>
1247 <p>
1248         gives
1249       </p>
1250 <p>
1251 </p>
1252 <pre class="programlisting"><span class="special">+</span><span class="identifier">L</span>      <span class="special">=</span> <span class="number">2</span> <span class="identifier">m</span> <span class="special">+</span> <span class="number">1</span> <span class="identifier">m</span> <span class="identifier">i</span>
1253 <span class="special">-</span><span class="identifier">L</span>      <span class="special">=</span> <span class="special">-</span><span class="number">2</span> <span class="identifier">m</span> <span class="special">+</span> <span class="special">-</span><span class="number">1</span> <span class="identifier">m</span> <span class="identifier">i</span>
1254 <span class="identifier">L</span><span class="special">+</span><span class="identifier">L</span>     <span class="special">=</span> <span class="number">4</span> <span class="identifier">m</span> <span class="special">+</span> <span class="number">2</span> <span class="identifier">m</span> <span class="identifier">i</span>
1255 <span class="identifier">L</span><span class="special">-</span><span class="identifier">L</span>     <span class="special">=</span> <span class="number">0</span> <span class="identifier">m</span> <span class="special">+</span> <span class="number">0</span> <span class="identifier">m</span> <span class="identifier">i</span>
1256 <span class="identifier">L</span><span class="special">*</span><span class="identifier">L</span>     <span class="special">=</span> <span class="number">3</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="special">+</span> <span class="number">4</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span> <span class="identifier">i</span>
1257 <span class="identifier">L</span><span class="special">/</span><span class="identifier">L</span>     <span class="special">=</span> <span class="number">1</span> <span class="identifier">dimensionless</span> <span class="special">+</span> <span class="number">0</span> <span class="identifier">dimensionless</span> <span class="identifier">i</span>
1258 <span class="identifier">L</span><span class="special">^</span><span class="number">3</span>     <span class="special">=</span> <span class="number">2</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span> <span class="special">+</span> <span class="number">11</span> <span class="identifier">m</span><span class="special">^</span><span class="number">3</span> <span class="identifier">i</span>
1259 <span class="identifier">L</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span> <span class="special">=</span> <span class="number">2.56713</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span> <span class="special">+</span> <span class="number">2.14247</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span> <span class="identifier">i</span>
1260 <span class="number">3</span><span class="identifier">vL</span>     <span class="special">=</span> <span class="number">1.29207</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">3</span><span class="special">)</span> <span class="special">+</span> <span class="number">0.201294</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">1</span><span class="special">/</span><span class="number">3</span><span class="special">)</span> <span class="identifier">i</span>
1261 <span class="special">(</span><span class="number">3</span><span class="special">/</span><span class="number">2</span><span class="special">)</span><span class="identifier">vL</span> <span class="special">=</span> <span class="number">1.62894</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">2</span><span class="special">/</span><span class="number">3</span><span class="special">)</span> <span class="special">+</span> <span class="number">0.520175</span> <span class="identifier">m</span><span class="special">^(</span><span class="number">2</span><span class="special">/</span><span class="number">3</span><span class="special">)</span> <span class="identifier">i</span>
1262 </pre>
1263 <p>
1264       </p>
1265 </div>
1266 <div class="section">
1267 <div class="titlepage"><div><div><h3 class="title">
1268 <a name="boost_units.Examples.PerformanceExample"></a><a class="link" href="Examples.html#boost_units.Examples.PerformanceExample" title="Performance Example">Performance
1269       Example</a>
1270 </h3></div></div></div>
1271 <p>
1272         (<a href="../../../libs/units/example/performance.cpp" target="_top">performance.cpp</a>)
1273       </p>
1274 <p>
1275         This example provides an ad hoc performance test to verify that zero runtime
1276         overhead is incurred when using <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/quantity.html" title="Class template quantity">quantity</a></code></span>
1277         in place of <code class="computeroutput"><span class="keyword">double</span></code>. Note that
1278         performance optimization and testing is not trivial, so some care must be
1279         taken in profiling. It is also critical to have a compiler capable of optimizing
1280         the many template instantiations and inline calls effectively to achieve
1281         maximal performance. Zero overhead for this test has been verified using
1282         gcc 4.0.1, and icc 9.0, 10.0, and 10.1 on Mac OS 10.4 and 10.5, and using
1283         msvc 8.0 on Windows XP.
1284       </p>
1285 </div>
1286 <div class="section">
1287 <div class="titlepage"><div><div><h3 class="title">
1288 <a name="boost_units.Examples.RadarBeamHeightExample"></a><a class="link" href="Examples.html#boost_units.Examples.RadarBeamHeightExample" title="Radar Beam Height">Radar Beam
1289       Height</a>
1290 </h3></div></div></div>
1291 <p>
1292         (<a href="../../../libs/units/example/radar_beam_height.cpp" target="_top">radar_beam_height.cpp</a>)
1293       </p>
1294 <p>
1295         This example demonstrates the implementation of two non-SI units of length,
1296         the nautical mile :
1297       </p>
1298 <p>
1299 </p>
1300 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">nautical</span> <span class="special">{</span>
1301
1302 <span class="keyword">struct</span> <span class="identifier">length_base_unit</span> <span class="special">:</span>
1303     <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">length_base_unit</span><span class="special">,</span> <span class="identifier">length_dimension</span><span class="special">,</span> <span class="number">1</span><span class="special">&gt;</span>
1304 <span class="special">{</span>
1305     <span class="keyword">static</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">name</span><span class="special">()</span>       <span class="special">{</span> <span class="keyword">return</span> <span class="string">"nautical mile"</span><span class="special">;</span> <span class="special">}</span>
1306     <span class="keyword">static</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">symbol</span><span class="special">()</span>     <span class="special">{</span> <span class="keyword">return</span> <span class="string">"nmi"</span><span class="special">;</span> <span class="special">}</span>
1307 <span class="special">};</span>
1308
1309 <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">make_system</span><span class="special">&lt;</span><span class="identifier">length_base_unit</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">system</span><span class="special">;</span>
1310
1311 <span class="comment">/// unit typedefs</span>
1312 <span class="keyword">typedef</span> <span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">system</span><span class="special">&gt;</span>    <span class="identifier">length</span><span class="special">;</span>
1313
1314 <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">length</span> <span class="identifier">mile</span><span class="special">,</span><span class="identifier">miles</span><span class="special">;</span>
1315
1316 <span class="special">}</span> <span class="comment">// namespace nautical</span>
1317
1318 <span class="comment">// helper for conversions between nautical length and si length</span>
1319 <span class="identifier">BOOST_UNITS_DEFINE_CONVERSION_FACTOR</span><span class="special">(</span><span class="identifier">nautical</span><span class="special">::</span><span class="identifier">length_base_unit</span><span class="special">,</span>
1320                                      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter_base_unit</span><span class="special">,</span>
1321                                      <span class="keyword">double</span><span class="special">,</span> <span class="number">1.852e3</span><span class="special">);</span>
1322 </pre>
1323 <p>
1324       </p>
1325 <p>
1326         and the imperial foot :
1327       </p>
1328 <p>
1329 </p>
1330 <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">imperial</span> <span class="special">{</span>
1331
1332 <span class="keyword">struct</span> <span class="identifier">length_base_unit</span> <span class="special">:</span>
1333     <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">length_base_unit</span><span class="special">,</span> <span class="identifier">length_dimension</span><span class="special">,</span> <span class="number">2</span><span class="special">&gt;</span>
1334 <span class="special">{</span>
1335     <span class="keyword">static</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">name</span><span class="special">()</span>       <span class="special">{</span> <span class="keyword">return</span> <span class="string">"foot"</span><span class="special">;</span> <span class="special">}</span>
1336     <span class="keyword">static</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">symbol</span><span class="special">()</span>     <span class="special">{</span> <span class="keyword">return</span> <span class="string">"ft"</span><span class="special">;</span> <span class="special">}</span>
1337 <span class="special">};</span>
1338
1339 <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">make_system</span><span class="special">&lt;</span><span class="identifier">length_base_unit</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">system</span><span class="special">;</span>
1340
1341 <span class="comment">/// unit typedefs</span>
1342 <span class="keyword">typedef</span> <span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">system</span><span class="special">&gt;</span>    <span class="identifier">length</span><span class="special">;</span>
1343
1344 <span class="keyword">static</span> <span class="keyword">const</span> <span class="identifier">length</span> <span class="identifier">foot</span><span class="special">,</span><span class="identifier">feet</span><span class="special">;</span>
1345
1346 <span class="special">}</span> <span class="comment">// imperial</span>
1347
1348 <span class="comment">// helper for conversions between imperial length and si length</span>
1349 <span class="identifier">BOOST_UNITS_DEFINE_CONVERSION_FACTOR</span><span class="special">(</span><span class="identifier">imperial</span><span class="special">::</span><span class="identifier">length_base_unit</span><span class="special">,</span>
1350                                      <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter_base_unit</span><span class="special">,</span>
1351                                      <span class="keyword">double</span><span class="special">,</span> <span class="number">1.0</span><span class="special">/</span><span class="number">3.28083989501312</span><span class="special">);</span>
1352 </pre>
1353 <p>
1354       </p>
1355 <p>
1356         These units include conversions between themselves and the meter. Three functions
1357         for computing radar beam height from radar range and the local earth radius
1358         are defined. The first takes arguments in one system and returns a value
1359         in the same system :
1360       </p>
1361 <p>
1362 </p>
1363 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">System</span><span class="special">,</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
1364 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">System</span><span class="special">&gt;,</span><span class="identifier">T</span><span class="special">&gt;</span>
1365 <span class="identifier">radar_beam_height</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">System</span><span class="special">&gt;,</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">radar_range</span><span class="special">,</span>
1366                   <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">System</span><span class="special">&gt;,</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">earth_radius</span><span class="special">,</span>
1367                   <span class="identifier">T</span> <span class="identifier">k</span> <span class="special">=</span> <span class="number">4.0</span><span class="special">/</span><span class="number">3.0</span><span class="special">)</span>
1368 <span class="special">{</span>
1369     <span class="keyword">return</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">System</span><span class="special">&gt;,</span><span class="identifier">T</span><span class="special">&gt;</span>
1370         <span class="special">(</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">radar_range</span><span class="special">)/(</span><span class="number">2.0</span><span class="special">*</span><span class="identifier">k</span><span class="special">*</span><span class="identifier">earth_radius</span><span class="special">));</span>
1371 <span class="special">}</span>
1372 </pre>
1373 <p>
1374       </p>
1375 <p>
1376         The second is similar, but is templated on return type, so that the arguments
1377         are converted to the return unit system internally :
1378       </p>
1379 <p>
1380 </p>
1381 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">return_type</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">System1</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">System2</span><span class="special">,</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
1382 <span class="identifier">return_type</span>
1383 <span class="identifier">radar_beam_height</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">System1</span><span class="special">&gt;,</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">radar_range</span><span class="special">,</span>
1384                   <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">length_dimension</span><span class="special">,</span><span class="identifier">System2</span><span class="special">&gt;,</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">earth_radius</span><span class="special">,</span>
1385                   <span class="identifier">T</span> <span class="identifier">k</span> <span class="special">=</span> <span class="number">4.0</span><span class="special">/</span><span class="number">3.0</span><span class="special">)</span>
1386 <span class="special">{</span>
1387     <span class="comment">// need to decide which system to use for calculation</span>
1388     <span class="keyword">const</span> <span class="identifier">return_type</span>   <span class="identifier">rr</span><span class="special">(</span><span class="identifier">radar_range</span><span class="special">),</span>
1389                         <span class="identifier">er</span><span class="special">(</span><span class="identifier">earth_radius</span><span class="special">);</span>
1390
1391     <span class="keyword">return</span> <span class="identifier">return_type</span><span class="special">(</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">rr</span><span class="special">)/(</span><span class="number">2.0</span><span class="special">*</span><span class="identifier">k</span><span class="special">*</span><span class="identifier">er</span><span class="special">));</span>
1392 <span class="special">}</span>
1393 </pre>
1394 <p>
1395       </p>
1396 <p>
1397         Finally, the third function is an empirical approximation that is only valid
1398         for radar ranges specified in nautical miles, returning beam height in feet.
1399         This function uses the heterogeneous unit of nautical miles per square root
1400         of feet to ensure dimensional correctness :
1401       </p>
1402 <p>
1403 </p>
1404 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">imperial</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span>
1405 <span class="identifier">radar_beam_height</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">nautical</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;&amp;</span> <span class="identifier">range</span><span class="special">)</span>
1406 <span class="special">{</span>
1407     <span class="keyword">return</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">imperial</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span>
1408         <span class="special">(</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">range</span><span class="special">/(</span><span class="number">1.23</span><span class="special">*</span><span class="identifier">nautical</span><span class="special">::</span><span class="identifier">miles</span><span class="special">/</span><span class="identifier">root</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">imperial</span><span class="special">::</span><span class="identifier">feet</span><span class="special">))));</span>
1409 <span class="special">}</span>
1410 </pre>
1411 <p>
1412       </p>
1413 <p>
1414         With these, we can compute radar beam height in various unit systems :
1415       </p>
1416 <p>
1417 </p>
1418 <pre class="programlisting"><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">nautical</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="identifier">radar_range</span><span class="special">(</span><span class="number">300.0</span><span class="special">*</span><span class="identifier">miles</span><span class="special">);</span>
1419 <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span>       <span class="identifier">earth_radius</span><span class="special">(</span><span class="number">6371.0087714</span><span class="special">*</span><span class="identifier">kilo</span><span class="special">*</span><span class="identifier">meters</span><span class="special">);</span>
1420
1421 <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span>       <span class="identifier">beam_height_1</span><span class="special">(</span><span class="identifier">radar_beam_height</span><span class="special">(</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;(</span><span class="identifier">radar_range</span><span class="special">),</span><span class="identifier">earth_radius</span><span class="special">));</span>
1422 <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">nautical</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="identifier">beam_height_2</span><span class="special">(</span><span class="identifier">radar_beam_height</span><span class="special">(</span><span class="identifier">radar_range</span><span class="special">,</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">nautical</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;(</span><span class="identifier">earth_radius</span><span class="special">)));</span>
1423 <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span>       <span class="identifier">beam_height_3</span><span class="special">(</span><span class="identifier">radar_beam_height</span><span class="special">&lt;</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="special">&gt;(</span><span class="identifier">radar_range</span><span class="special">,</span><span class="identifier">earth_radius</span><span class="special">));</span>
1424 <span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">nautical</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="identifier">beam_height_4</span><span class="special">(</span><span class="identifier">radar_beam_height</span><span class="special">&lt;</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">nautical</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="special">&gt;(</span><span class="identifier">radar_range</span><span class="special">,</span><span class="identifier">earth_radius</span><span class="special">));</span>
1425 </pre>
1426 <p>
1427       </p>
1428 <p>
1429         giving
1430       </p>
1431 <p>
1432 </p>
1433 <pre class="programlisting"><span class="identifier">radar</span> <span class="identifier">range</span>        <span class="special">:</span> <span class="number">300</span> <span class="identifier">nmi</span>
1434 <span class="identifier">earth</span> <span class="identifier">radius</span>       <span class="special">:</span> <span class="number">6.37101e+06</span> <span class="identifier">m</span>
1435 <span class="identifier">beam</span> <span class="identifier">height</span> <span class="number">1</span>      <span class="special">:</span> <span class="number">18169.7</span> <span class="identifier">m</span>
1436 <span class="identifier">beam</span> <span class="identifier">height</span> <span class="number">2</span>      <span class="special">:</span> <span class="number">9.81085</span> <span class="identifier">nmi</span>
1437 <span class="identifier">beam</span> <span class="identifier">height</span> <span class="number">3</span>      <span class="special">:</span> <span class="number">18169.7</span> <span class="identifier">m</span>
1438 <span class="identifier">beam</span> <span class="identifier">height</span> <span class="number">4</span>      <span class="special">:</span> <span class="number">9.81085</span> <span class="identifier">nmi</span>
1439 <span class="identifier">beam</span> <span class="identifier">height</span> <span class="identifier">approx</span> <span class="special">:</span> <span class="number">59488.4</span> <span class="identifier">ft</span>
1440 <span class="identifier">beam</span> <span class="identifier">height</span> <span class="identifier">approx</span> <span class="special">:</span> <span class="number">18132.1</span> <span class="identifier">m</span>
1441 </pre>
1442 <p>
1443       </p>
1444 </div>
1445 <div class="section">
1446 <div class="titlepage"><div><div><h3 class="title">
1447 <a name="boost_units.Examples.HeterogeneousUnitExample"></a><a class="link" href="Examples.html#boost_units.Examples.HeterogeneousUnitExample" title="Heterogeneous Unit Example">Heterogeneous
1448       Unit Example</a>
1449 </h3></div></div></div>
1450 <p>
1451         (<a href="../../../libs/units/example/heterogeneous_unit.cpp" target="_top">heterogeneous_unit.cpp</a>)
1452       </p>
1453 <p>
1454         Mixed units and mixed unit conversions.
1455       </p>
1456 <p>
1457         This code:
1458       </p>
1459 <p>
1460 </p>
1461 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span>        <span class="identifier">L</span><span class="special">(</span><span class="number">1.5</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">);</span>
1462 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">mass</span><span class="special">&gt;</span>         <span class="identifier">M</span><span class="special">(</span><span class="number">1.0</span><span class="special">*</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">gram</span><span class="special">);</span>
1463
1464 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">L</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span>
1465           <span class="special">&lt;&lt;</span> <span class="identifier">M</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span>
1466           <span class="special">&lt;&lt;</span> <span class="identifier">L</span><span class="special">*</span><span class="identifier">M</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span>
1467           <span class="special">&lt;&lt;</span> <span class="identifier">L</span><span class="special">/</span><span class="identifier">M</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span>
1468           <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1469
1470 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="number">1.0</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">kilogram</span><span class="special">/</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span>
1471           <span class="special">&lt;&lt;</span> <span class="number">1.0</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">kilogram</span><span class="special">/</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span><span class="special">)/</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span>
1472           <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1473
1474 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="number">1.0</span><span class="special">*</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">centimeter</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">kilogram</span><span class="special">/</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span>
1475           <span class="special">&lt;&lt;</span> <span class="number">1.0</span><span class="special">*</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">centimeter</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">kilogram</span><span class="special">/</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span><span class="special">)/</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span>
1476           <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1477 </pre>
1478 <p>
1479       </p>
1480 <p>
1481         gives
1482       </p>
1483 <p>
1484 </p>
1485 <pre class="programlisting"><span class="number">1.5</span> <span class="identifier">m</span>
1486 <span class="number">1</span> <span class="identifier">g</span>
1487 <span class="number">1.5</span> <span class="identifier">m</span> <span class="identifier">g</span>
1488 <span class="number">1.5</span> <span class="identifier">m</span> <span class="identifier">g</span><span class="special">^-</span><span class="number">1</span>
1489
1490 <span class="number">1</span> <span class="identifier">N</span>
1491 <span class="number">1</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span>
1492
1493 <span class="number">1</span> <span class="identifier">cm</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span>
1494 <span class="number">1</span> <span class="identifier">cm</span> <span class="identifier">m</span><span class="special">^-</span><span class="number">1</span> <span class="identifier">kg</span> <span class="identifier">s</span><span class="special">^-</span><span class="number">2</span>
1495 </pre>
1496 <p>
1497       </p>
1498 <p>
1499         Arbitrary conversions also work:
1500       </p>
1501 <p>
1502 </p>
1503 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">area</span><span class="special">&gt;</span>      <span class="identifier">A</span><span class="special">(</span><span class="number">1.5</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">*</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">centimeter</span><span class="special">);</span>
1504
1505 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="number">1.5</span><span class="special">*</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">*</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">centimeter</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span>
1506           <span class="special">&lt;&lt;</span> <span class="identifier">A</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span>
1507           <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1508 </pre>
1509 <p>
1510       </p>
1511 <p>
1512         yielding
1513       </p>
1514 <p>
1515 </p>
1516 <pre class="programlisting"><span class="number">1.5</span> <span class="identifier">cm</span> <span class="identifier">m</span>
1517 <span class="number">0.015</span> <span class="identifier">m</span><span class="special">^</span><span class="number">2</span>
1518 </pre>
1519 <p>
1520       </p>
1521 </div>
1522 <div class="section">
1523 <div class="titlepage"><div><div><h3 class="title">
1524 <a name="boost_units.Examples.AbsoluteRelativeTemperatureExample"></a><a class="link" href="Examples.html#boost_units.Examples.AbsoluteRelativeTemperatureExample" title="Absolute and Relative Temperature Example">Absolute
1525       and Relative Temperature Example</a>
1526 </h3></div></div></div>
1527 <p>
1528         (<a href="../../../libs/units/example/temperature.cpp" target="_top">temperature.cpp</a>)
1529       </p>
1530 <p>
1531         This example demonstrates using of absolute temperatures and relative temperature
1532         differences in Fahrenheit and converting between these and the Kelvin temperature
1533         scale. This issue touches on some surprisingly deep mathematical concepts
1534         (see <a href="http://en.wikipedia.org/wiki/Affine_space" target="_top">Wikipedia</a>
1535         for a basic review), but for our purposes here, we will simply observe that
1536         it is important to be able to differentiate between an absolute temperature
1537         measurement and a measurement of temperature difference. This is accomplished
1538         by using the <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/absolute.html" title="Class template absolute">absolute</a></code></span>
1539         wrapper class.
1540       </p>
1541 <p>
1542         First we define a system using the predefined fahrenheit base unit:
1543       </p>
1544 <p>
1545 </p>
1546 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">temperature</span><span class="special">::</span><span class="identifier">fahrenheit_base_unit</span><span class="special">::</span><span class="identifier">unit_type</span>    <span class="identifier">temperature</span><span class="special">;</span>
1547 <span class="keyword">typedef</span> <span class="identifier">get_system</span><span class="special">&lt;</span><span class="identifier">temperature</span><span class="special">&gt;::</span><span class="identifier">type</span>                   <span class="identifier">system</span><span class="special">;</span>
1548
1549 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">degree</span><span class="special">,</span><span class="identifier">temperature</span><span class="special">);</span>
1550 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">degrees</span><span class="special">,</span><span class="identifier">temperature</span><span class="special">);</span>
1551 </pre>
1552 <p>
1553       </p>
1554 <p>
1555         Now we can create some quantities:
1556       </p>
1557 <p>
1558 </p>
1559 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">absolute</span><span class="special">&lt;</span><span class="identifier">fahrenheit</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;</span> <span class="special">&gt;</span>    <span class="identifier">T1p</span><span class="special">(</span>
1560     <span class="number">32.0</span><span class="special">*</span><span class="identifier">absolute</span><span class="special">&lt;</span><span class="identifier">fahrenheit</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;());</span>
1561 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">fahrenheit</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;</span>               <span class="identifier">T1v</span><span class="special">(</span>
1562     <span class="number">32.0</span><span class="special">*</span><span class="identifier">fahrenheit</span><span class="special">::</span><span class="identifier">degrees</span><span class="special">);</span>
1563
1564 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">absolute</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;</span> <span class="special">&gt;</span>            <span class="identifier">T2p</span><span class="special">(</span><span class="identifier">T1p</span><span class="special">);</span>
1565 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;</span>                       <span class="identifier">T2v</span><span class="special">(</span><span class="identifier">T1v</span><span class="special">);</span>
1566 </pre>
1567 <p>
1568       </p>
1569 <p>
1570         Note the use of <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/absolute.html" title="Class template absolute">absolute</a></code></span>
1571         to wrap a unit. The resulting output is:
1572       </p>
1573 <p>
1574 </p>
1575 <pre class="programlisting"><span class="special">{</span> <span class="number">32</span> <span class="special">}</span> <span class="identifier">F</span>
1576 <span class="special">{</span> <span class="number">273.15</span> <span class="special">}</span> <span class="identifier">K</span>
1577 <span class="special">{</span> <span class="number">273.15</span> <span class="special">}</span> <span class="identifier">K</span>
1578 <span class="special">[</span> <span class="number">32</span> <span class="special">]</span> <span class="identifier">F</span>
1579 <span class="special">[</span> <span class="number">17.7778</span> <span class="special">]</span> <span class="identifier">K</span>
1580 <span class="special">[</span> <span class="number">17.7778</span> <span class="special">]</span> <span class="identifier">K</span>
1581 </pre>
1582 <p>
1583       </p>
1584 </div>
1585 <div class="section">
1586 <div class="titlepage"><div><div><h3 class="title">
1587 <a name="boost_units.Examples.RuntimeConversionFactorExample"></a><a class="link" href="Examples.html#boost_units.Examples.RuntimeConversionFactorExample" title="Runtime Conversion Factor Example">Runtime
1588       Conversion Factor Example</a>
1589 </h3></div></div></div>
1590 <p>
1591         (<a href="../../../libs/units/example/runtime_conversion_factor.cpp" target="_top">runtime_conversion_factor.cpp</a>)
1592       </p>
1593 <p>
1594         The Boost.Units library does not require that the conversion factors be compile
1595         time constants, as is demonstrated in this example:
1596       </p>
1597 <p>
1598 </p>
1599 <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">base_dimension</span><span class="special">;</span>
1600 <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">base_unit</span><span class="special">;</span>
1601
1602 <span class="keyword">static</span> <span class="keyword">const</span> <span class="keyword">long</span> <span class="identifier">currency_base</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span>
1603
1604 <span class="keyword">struct</span> <span class="identifier">currency_base_dimension</span> <span class="special">:</span> <span class="identifier">base_dimension</span><span class="special">&lt;</span><span class="identifier">currency_base_dimension</span><span class="special">,</span> <span class="number">1</span><span class="special">&gt;</span> <span class="special">{};</span>
1605
1606 <span class="keyword">typedef</span> <span class="identifier">currency_base_dimension</span><span class="special">::</span><span class="identifier">dimension_type</span> <span class="identifier">currency_type</span><span class="special">;</span>
1607
1608 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="identifier">N</span><span class="special">&gt;</span>
1609 <span class="keyword">struct</span> <span class="identifier">currency_base_unit</span> <span class="special">:</span>
1610     <span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">currency_base_unit</span><span class="special">&lt;</span><span class="identifier">N</span><span class="special">&gt;,</span> <span class="identifier">currency_type</span><span class="special">,</span> <span class="identifier">currency_base</span> <span class="special">+</span> <span class="identifier">N</span><span class="special">&gt;</span> <span class="special">{};</span>
1611
1612 <span class="keyword">typedef</span> <span class="identifier">currency_base_unit</span><span class="special">&lt;</span><span class="number">0</span><span class="special">&gt;</span> <span class="identifier">us_dollar_base_unit</span><span class="special">;</span>
1613 <span class="keyword">typedef</span> <span class="identifier">currency_base_unit</span><span class="special">&lt;</span><span class="number">1</span><span class="special">&gt;</span> <span class="identifier">euro_base_unit</span><span class="special">;</span>
1614
1615 <span class="keyword">typedef</span> <span class="identifier">us_dollar_base_unit</span><span class="special">::</span><span class="identifier">unit_type</span> <span class="identifier">us_dollar</span><span class="special">;</span>
1616 <span class="keyword">typedef</span> <span class="identifier">euro_base_unit</span><span class="special">::</span><span class="identifier">unit_type</span> <span class="identifier">euro</span><span class="special">;</span>
1617
1618 <span class="comment">// an array of all possible conversions</span>
1619 <span class="keyword">double</span> <span class="identifier">conversion_factors</span><span class="special">[</span><span class="number">2</span><span class="special">][</span><span class="number">2</span><span class="special">]</span> <span class="special">=</span> <span class="special">{</span>
1620     <span class="special">{</span><span class="number">1.0</span><span class="special">,</span> <span class="number">1.0</span><span class="special">},</span>
1621     <span class="special">{</span><span class="number">1.0</span><span class="special">,</span> <span class="number">1.0</span><span class="special">}</span>
1622 <span class="special">};</span>
1623
1624 <span class="keyword">double</span> <span class="identifier">get_conversion_factor</span><span class="special">(</span><span class="keyword">long</span> <span class="identifier">from</span><span class="special">,</span> <span class="keyword">long</span> <span class="identifier">to</span><span class="special">)</span> <span class="special">{</span>
1625     <span class="keyword">return</span><span class="special">(</span><span class="identifier">conversion_factors</span><span class="special">[</span><span class="identifier">from</span><span class="special">][</span><span class="identifier">to</span><span class="special">]);</span>
1626 <span class="special">}</span>
1627
1628 <span class="keyword">void</span> <span class="identifier">set_conversion_factor</span><span class="special">(</span><span class="keyword">long</span> <span class="identifier">from</span><span class="special">,</span> <span class="keyword">long</span> <span class="identifier">to</span><span class="special">,</span> <span class="keyword">double</span> <span class="identifier">value</span><span class="special">)</span> <span class="special">{</span>
1629     <span class="identifier">conversion_factors</span><span class="special">[</span><span class="identifier">from</span><span class="special">][</span><span class="identifier">to</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">value</span><span class="special">;</span>
1630     <span class="identifier">conversion_factors</span><span class="special">[</span><span class="identifier">to</span><span class="special">][</span><span class="identifier">from</span><span class="special">]</span> <span class="special">=</span> <span class="number">1.0</span> <span class="special">/</span> <span class="identifier">value</span><span class="special">;</span>
1631 <span class="special">}</span>
1632
1633 <span class="identifier">BOOST_UNITS_DEFINE_CONVERSION_FACTOR_TEMPLATE</span><span class="special">((</span><span class="keyword">long</span> <span class="identifier">N1</span><span class="special">)(</span><span class="keyword">long</span> <span class="identifier">N2</span><span class="special">),</span>
1634     <span class="identifier">currency_base_unit</span><span class="special">&lt;</span><span class="identifier">N1</span><span class="special">&gt;,</span>
1635     <span class="identifier">currency_base_unit</span><span class="special">&lt;</span><span class="identifier">N2</span><span class="special">&gt;,</span>
1636     <span class="keyword">double</span><span class="special">,</span> <span class="identifier">get_conversion_factor</span><span class="special">(</span><span class="identifier">N1</span><span class="special">,</span> <span class="identifier">N2</span><span class="special">));</span>
1637 </pre>
1638 <p>
1639       </p>
1640 </div>
1641 <div class="section">
1642 <div class="titlepage"><div><div><h3 class="title">
1643 <a name="boost_units.Examples.UnitsWithNonbaseDimensions"></a><a class="link" href="Examples.html#boost_units.Examples.UnitsWithNonbaseDimensions" title="Units with Non-base Dimensions">Units
1644       with Non-base Dimensions</a>
1645 </h3></div></div></div>
1646 <p>
1647         (<a href="../../../libs/units/example/non_base_dimension.cpp" target="_top">non_base_dimension.cpp</a>)
1648       </p>
1649 <p>
1650         It is also possible to define base units that have derived rather than base
1651         dimensions:
1652       </p>
1653 <p>
1654 </p>
1655 <pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">imperial_gallon_tag</span> <span class="special">:</span>
1656     <span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">imperial_gallon_tag</span><span class="special">,</span> <span class="identifier">volume_dimension</span><span class="special">,</span> <span class="number">1</span><span class="special">&gt;</span> <span class="special">{</span> <span class="special">};</span>
1657
1658 <span class="keyword">typedef</span> <span class="identifier">make_system</span><span class="special">&lt;</span><span class="identifier">imperial_gallon_tag</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">imperial</span><span class="special">;</span>
1659
1660 <span class="keyword">typedef</span> <span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">volume_dimension</span><span class="special">,</span><span class="identifier">imperial</span><span class="special">&gt;</span> <span class="identifier">imperial_gallon</span><span class="special">;</span>
1661
1662 <span class="keyword">struct</span> <span class="identifier">us_gallon_tag</span> <span class="special">:</span> <span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">us_gallon_tag</span><span class="special">,</span> <span class="identifier">volume_dimension</span><span class="special">,</span> <span class="number">2</span><span class="special">&gt;</span> <span class="special">{</span> <span class="special">};</span>
1663
1664 <span class="keyword">typedef</span> <span class="identifier">make_system</span><span class="special">&lt;</span><span class="identifier">us_gallon_tag</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">us</span><span class="special">;</span>
1665
1666 <span class="keyword">typedef</span> <span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">volume_dimension</span><span class="special">,</span><span class="identifier">us</span><span class="special">&gt;</span> <span class="identifier">us_gallon</span><span class="special">;</span>
1667 </pre>
1668 <p>
1669       </p>
1670 </div>
1671 <div class="section">
1672 <div class="titlepage"><div><div><h3 class="title">
1673 <a name="boost_units.Examples.OutputForCompositeUnits"></a><a class="link" href="Examples.html#boost_units.Examples.OutputForCompositeUnits" title="Output for Composite Units">Output
1674       for Composite Units</a>
1675 </h3></div></div></div>
1676 <p>
1677         (<a href="../../../libs/units/example/composite_output.cpp" target="_top">composite_output.cpp</a>)
1678       </p>
1679 <p>
1680         If a unit has a special name and/or symbol, the free functions <code class="computeroutput"><span class="identifier">name_string</span></code> and <code class="computeroutput"><span class="identifier">symbol_string</span></code>
1681         can be overloaded directly.
1682       </p>
1683 <p>
1684 </p>
1685 <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">name_string</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">cgs</span><span class="special">::</span><span class="identifier">force</span><span class="special">&amp;)</span>
1686 <span class="special">{</span>
1687     <span class="keyword">return</span> <span class="string">"dyne"</span><span class="special">;</span>
1688 <span class="special">}</span>
1689
1690 <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">symbol_string</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">cgs</span><span class="special">::</span><span class="identifier">force</span><span class="special">&amp;)</span>
1691 <span class="special">{</span>
1692     <span class="keyword">return</span> <span class="string">"dyn"</span><span class="special">;</span>
1693 <span class="special">}</span>
1694 </pre>
1695 <p>
1696       </p>
1697 <p>
1698         In this case, any unit that reduces to the overloaded unit will be output
1699         with the replacement symbol.
1700       </p>
1701 <p>
1702         Special names and symbols for the SI and CGS unit systems are found in <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.systems.si.io_hpp" title="Header &lt;boost/units/systems/si/io.hpp&gt;">boost/units/systems/si/io.hpp</a></code>
1703         and <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.systems.cgs.io_hpp" title="Header &lt;boost/units/systems/cgs/io.hpp&gt;">boost/units/systems/cgs/io.hpp</a></code>,
1704         respectively. If these headers are not included, the output will simply follow
1705         default rules using the appropriate fundamental dimensions. Note that neither
1706         of these functions is defined for quantities because doing so would require
1707         making assumptions on how the corresponding value type should be formatted.
1708       </p>
1709 <p>
1710         Three <code class="computeroutput"><span class="identifier">ostream</span></code> formatters,
1711         <code class="computeroutput"><span class="identifier">symbol_format</span></code>, <code class="computeroutput"><span class="identifier">name_format</span></code>, and <code class="computeroutput"><span class="identifier">typename_format</span></code>
1712         are provided for convenience. These select the textual representation of
1713         units provided by <code class="computeroutput"><span class="identifier">symbol_string</span></code>
1714         or <code class="computeroutput"><span class="identifier">name_string</span></code> in the first
1715         two cases, while the latter returns a demangled typename for debugging purposes.
1716         Formatting of scaled unit is also done correctly.
1717       </p>
1718 </div>
1719 <div class="section">
1720 <div class="titlepage"><div><div><h3 class="title">
1721 <a name="boost_units.Examples.autoscale"></a><a class="link" href="Examples.html#boost_units.Examples.autoscale" title="Automatically Scaled Units">Automatically Scaled
1722       Units</a>
1723 </h3></div></div></div>
1724 <p>
1725         It is often desirable to scale a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/unit.html" title="Class template unit">unit</a></code></span>
1726         automatically, depending on its value, to keep the integral part in a limited
1727         range, usually between 1 and 999.
1728       </p>
1729 <p>
1730         For example, using <a href="http://en.wikipedia.org/wiki/Engineering_notation" target="_top">engineering
1731         notation prefixes</a>,
1732       </p>
1733 <pre class="programlisting"><span class="string">"1234.5 m"</span> <span class="identifier">is</span> <span class="identifier">more</span> <span class="identifier">helpfully</span> <span class="identifier">displayed</span> <span class="identifier">as</span> <span class="string">"1.234 km"</span>
1734 <span class="string">"0.000000001234 m"</span> <span class="identifier">is</span> <span class="identifier">more</span> <span class="identifier">clearly</span> <span class="identifier">displayed</span> <span class="identifier">as</span> <span class="string">"1.2345 nanometer"</span><span class="special">.</span>
1735 </pre>
1736 <p>
1737         The iostream manipulators <code class="computeroutput"><span class="identifier">engineering_prefixes</span></code>
1738         or <code class="computeroutput"><span class="identifier">binary_prefixes</span></code> make this
1739         easy.
1740       </p>
1741 <p>
1742 </p>
1743 <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">binary_prefix</span><span class="special">;</span>
1744 <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">engineering_prefix</span><span class="special">;</span>
1745 <span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">no_prefix</span><span class="special">;</span>
1746
1747 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="identifier">l</span> <span class="special">=</span> <span class="number">2.345</span> <span class="special">*</span> <span class="identifier">meters</span><span class="special">;</span>   <span class="comment">// A quantity of length, in units of meters.</span>
1748 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">engineering_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Outputs "2.345 m".</span>
1749 <span class="identifier">l</span> <span class="special">=</span>  <span class="number">1000.0</span> <span class="special">*</span> <span class="identifier">l</span><span class="special">;</span> <span class="comment">// Increase it by 1000, so expect a k prefix.</span>
1750 <span class="comment">// Note that a double 1000.0 is required - an integer will fail to compile.</span>
1751 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">engineering_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Output autoprefixed with k to "2.345 km".</span>
1752
1753 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">energy</span><span class="special">&gt;</span> <span class="identifier">e</span> <span class="special">=</span> <span class="identifier">kilograms</span> <span class="special">*</span> <span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;(</span><span class="identifier">l</span> <span class="special">/</span> <span class="identifier">seconds</span><span class="special">);</span> <span class="comment">// A quantity of energy.</span>
1754 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">engineering_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 5.49902 MJ</span>
1755 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">name_format</span> <span class="special">&lt;&lt;</span> <span class="identifier">engineering_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">e</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 5.49902 megaJoule</span>
1756 </pre>
1757 <p>
1758       </p>
1759 <p>
1760         (The complete set of <a href="http://physics.nist.gov/cuu/Units/prefixes.html" target="_top">engineering
1761         and scientific multiples</a> is not used (not centi or deci for example),
1762         but only powers of ten that are multiples of three, 10^3).
1763       </p>
1764 <p>
1765         Similarly, the equivalent <a href="http://en.wikipedia.org/wiki/Binary_prefixes" target="_top">binary
1766         prefixes</a> used for displaying computing kilobytes, megabytes, gigabytes...
1767       </p>
1768 <p>
1769         These are the 2^10 = 1024, 2^20 = 1 048 576, 2^30 ... multiples.
1770       </p>
1771 <p>
1772         (See also <a href="http://physics.nist.gov/cuu/Units/binary.html" target="_top">Prefixes
1773         for binary multiples</a>
1774       </p>
1775 <p>
1776         This scale is specified in IEC 60027-2, Second edition, 2000-11, Letter symbols
1777         to be used in electrical technology - Part 2: Telecommunications and electronics).
1778       </p>
1779 <p>
1780 </p>
1781 <pre class="programlisting"><span class="comment">// Don't forget that the units name or symbol format specification is persistent.</span>
1782 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">symbol_format</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Resets the format to the default symbol format.</span>
1783
1784 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">byte_base_unit</span><span class="special">::</span><span class="identifier">unit_type</span><span class="special">&gt;</span> <span class="identifier">b</span> <span class="special">=</span> <span class="number">2048.</span> <span class="special">*</span> <span class="identifier">byte_base_unit</span><span class="special">::</span><span class="identifier">unit_type</span><span class="special">();</span>
1785 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">engineering_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">b</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>  <span class="comment">// 2.048 kb</span>
1786 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">symbol_format</span> <span class="special">&lt;&lt;</span> <span class="identifier">binary_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">b</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">//  "2 Kib"</span>
1787 </pre>
1788 <p>
1789       </p>
1790 <p>
1791         But note that scalar dimensionless values, like int, float and double, are
1792         <span class="bold"><strong>not</strong></span> prefixed automatically by the engineering_prefix
1793         or binary_prefix iostream manipulators.
1794       </p>
1795 <p>
1796 </p>
1797 <pre class="programlisting"><span class="keyword">const</span> <span class="keyword">double</span> <span class="identifier">s1</span> <span class="special">=</span> <span class="number">2345.6</span><span class="special">;</span>
1798 <span class="keyword">const</span> <span class="keyword">long</span> <span class="identifier">x1</span> <span class="special">=</span> <span class="number">23456</span><span class="special">;</span>
1799 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">engineering_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">s1</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 2345.6</span>
1800 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">engineering_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">x1</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 23456</span>
1801
1802 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">binary_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">s1</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 2345.6</span>
1803 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">binary_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">x1</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 23456</span>
1804 </pre>
1805 <p>
1806       </p>
1807 <p>
1808         You can output the name or symbol of a unit (rather than the most common
1809         quantity of a unit).
1810       </p>
1811 <p>
1812 </p>
1813 <pre class="programlisting"><span class="keyword">const</span> <span class="identifier">length</span> <span class="identifier">L</span><span class="special">;</span> <span class="comment">// A unit of length (but not a quantity of length).</span>
1814 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">L</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Default length unit is meter,</span>
1815 <span class="comment">// but default is symbol format so output is just "m".</span>
1816 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">name_format</span> <span class="special">&lt;&lt;</span> <span class="identifier">L</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// default length name is "meter".</span>
1817 </pre>
1818 <p>
1819       </p>
1820 <p>
1821         Note too that all the formatting flags are persistent, so that if you set
1822         engineering_prefix, then it applies to all future outputs, until you select
1823         binary_prefix, or explicitly switch autoprefix off. You can specify no prefix
1824         (the default of course) in two ways:
1825       </p>
1826 <p>
1827 </p>
1828 <pre class="programlisting"><span class="identifier">no_prefix</span><span class="special">(</span><span class="identifier">cout</span><span class="special">);</span> <span class="comment">// Clear any prefix flag.</span>
1829 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">no_prefix</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// Clear any prefix flag using `no_prefix` manipulator.</span>
1830 </pre>
1831 <p>
1832       </p>
1833 <p>
1834         And you can get the format flags for diagnosing problems.
1835       </p>
1836 <p>
1837 </p>
1838 <pre class="programlisting"><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">get_autoprefix</span><span class="special">(</span><span class="identifier">cout</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 8 is `autoprefix_binary` from `enum autoprefix_mode`.</span>
1839 <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">get_format</span><span class="special">(</span><span class="identifier">cout</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span> <span class="comment">// 1 is `name_fmt` from `enum format_mode`.</span>
1840 </pre>
1841 <p>
1842       </p>
1843 </div>
1844 <div class="section">
1845 <div class="titlepage"><div><div><h3 class="title">
1846 <a name="boost_units.Examples.ConversionFactor"></a><a class="link" href="Examples.html#boost_units.Examples.ConversionFactor" title="Conversion Factor">Conversion Factor</a>
1847 </h3></div></div></div>
1848 <p>
1849         This code demonstrates the use of the <code class="computeroutput"><span class="identifier">conversion_factor</span></code>
1850         free function to determine the scale factor between two units.
1851       </p>
1852 <p>
1853         (<a href="../../../libs/units/example/conversion_factor.cpp" target="_top">conversion_factor.cpp</a>)
1854       </p>
1855 <p>
1856 </p>
1857 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">dyne_to_newton</span> <span class="special">=</span>
1858     <span class="identifier">conversion_factor</span><span class="special">(</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">dyne</span><span class="special">,</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">newton</span><span class="special">);</span>
1859 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">dyne_to_newton</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1860
1861 <span class="keyword">double</span> <span class="identifier">force_over_mass_conversion</span> <span class="special">=</span>
1862     <span class="identifier">conversion_factor</span><span class="special">(</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">newton</span><span class="special">/</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">kilogram</span><span class="special">,</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">dyne</span><span class="special">/</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">gram</span><span class="special">);</span>
1863 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">force_over_mass_conversion</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1864
1865 <span class="keyword">double</span> <span class="identifier">momentum_conversion</span> <span class="special">=</span>
1866     <span class="identifier">conversion_factor</span><span class="special">(</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">momentum</span><span class="special">(),</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">momentum</span><span class="special">());</span>
1867 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">momentum_conversion</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1868
1869 <span class="keyword">double</span> <span class="identifier">momentum_over_mass_conversion</span> <span class="special">=</span>
1870     <span class="identifier">conversion_factor</span><span class="special">(</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">momentum</span><span class="special">()/</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">mass</span><span class="special">(),</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">momentum</span><span class="special">()/</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">gram</span><span class="special">);</span>
1871 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">momentum_over_mass_conversion</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1872
1873 <span class="keyword">double</span> <span class="identifier">acceleration_conversion</span> <span class="special">=</span>
1874     <span class="identifier">conversion_factor</span><span class="special">(</span><span class="identifier">cgs</span><span class="special">::</span><span class="identifier">gal</span><span class="special">,</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">meter_per_second_squared</span><span class="special">);</span>
1875 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">acceleration_conversion</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1876 </pre>
1877 <p>
1878       </p>
1879 <p>
1880         Produces
1881       </p>
1882 <p>
1883 </p>
1884 <pre class="programlisting"><span class="number">1e-005</span>
1885 <span class="number">100</span>
1886 <span class="number">1e-005</span>
1887 <span class="number">100</span>
1888 <span class="number">0.01</span>
1889 </pre>
1890 <p>
1891       </p>
1892 </div>
1893 <div class="section">
1894 <div class="titlepage"><div><div><h3 class="title">
1895 <a name="boost_units.Examples.RuntimeUnits"></a><a class="link" href="Examples.html#boost_units.Examples.RuntimeUnits" title="Runtime Units">Runtime Units</a>
1896 </h3></div></div></div>
1897 <p>
1898         (<a href="../../../libs/units/example/runtime_unit.cpp" target="_top">runtime_unit.cpp</a>)
1899       </p>
1900 <p>
1901         This example shows how to implement an interface that allow different units
1902         at runtime while still maintaining type safety for internal calculations.
1903       </p>
1904 <p>
1905 </p>
1906 <pre class="programlisting"><span class="keyword">namespace</span> <span class="special">{</span>
1907
1908 <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">;</span>
1909 <span class="keyword">using</span> <span class="identifier">imperial</span><span class="special">::</span><span class="identifier">foot_base_unit</span><span class="special">;</span>
1910
1911 <span class="identifier">std</span><span class="special">::</span><span class="identifier">map</span><span class="special">&lt;</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span><span class="special">,</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">known_units</span><span class="special">;</span>
1912
1913 <span class="special">}</span>
1914
1915 <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="identifier">calculate</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;&amp;</span> <span class="identifier">t</span><span class="special">)</span>
1916 <span class="special">{</span>
1917     <span class="keyword">return</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">hypot</span><span class="special">(</span><span class="identifier">t</span><span class="special">,</span> <span class="number">2.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meters</span><span class="special">));</span>
1918 <span class="special">}</span>
1919
1920 <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
1921 <span class="special">{</span>
1922     <span class="identifier">known_units</span><span class="special">[</span><span class="string">"meter"</span><span class="special">]</span> <span class="special">=</span> <span class="number">1.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meters</span><span class="special">;</span>
1923     <span class="identifier">known_units</span><span class="special">[</span><span class="string">"centimeter"</span><span class="special">]</span> <span class="special">=</span> <span class="special">.</span><span class="number">01</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meters</span><span class="special">;</span>
1924     <span class="identifier">known_units</span><span class="special">[</span><span class="string">"foot"</span><span class="special">]</span> <span class="special">=</span>
1925         <span class="identifier">conversion_factor</span><span class="special">(</span><span class="identifier">foot_base_unit</span><span class="special">::</span><span class="identifier">unit_type</span><span class="special">(),</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">;</span>
1926
1927     <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">output_type</span><span class="special">(</span><span class="string">"meter"</span><span class="special">);</span>
1928     <span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">input</span><span class="special">;</span>
1929
1930     <span class="keyword">while</span><span class="special">((</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"&gt; "</span><span class="special">)</span> <span class="special">&amp;&amp;</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span> <span class="special">&gt;&gt;</span> <span class="identifier">input</span><span class="special">))</span>
1931     <span class="special">{</span>
1932         <span class="keyword">if</span><span class="special">(!</span><span class="identifier">input</span><span class="special">.</span><span class="identifier">empty</span><span class="special">()</span> <span class="special">&amp;&amp;</span> <span class="identifier">input</span><span class="special">[</span><span class="number">0</span><span class="special">]</span> <span class="special">==</span> <span class="char">'#'</span><span class="special">)</span>
1933         <span class="special">{</span>
1934             <span class="identifier">std</span><span class="special">::</span><span class="identifier">getline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span><span class="special">,</span> <span class="identifier">input</span><span class="special">);</span>
1935         <span class="special">}</span>
1936         <span class="keyword">else</span> <span class="keyword">if</span><span class="special">(</span><span class="identifier">input</span> <span class="special">==</span> <span class="string">"exit"</span><span class="special">)</span>
1937         <span class="special">{</span>
1938             <span class="keyword">break</span><span class="special">;</span>
1939         <span class="special">}</span>
1940         <span class="keyword">else</span> <span class="keyword">if</span><span class="special">(</span><span class="identifier">input</span> <span class="special">==</span> <span class="string">"help"</span><span class="special">)</span>
1941         <span class="special">{</span>
1942             <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"type \"exit\" to exit\n"</span>
1943                 <span class="string">"type \"return 'unit'\" to set the return units\n"</span>
1944                 <span class="string">"type \"'number' 'unit'\" to do a simple calculation"</span>
1945                 <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1946         <span class="special">}</span>
1947         <span class="keyword">else</span> <span class="keyword">if</span><span class="special">(</span><span class="identifier">input</span> <span class="special">==</span> <span class="string">"return"</span><span class="special">)</span>
1948         <span class="special">{</span>
1949             <span class="keyword">if</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span> <span class="special">&gt;&gt;</span> <span class="identifier">input</span><span class="special">)</span>
1950             <span class="special">{</span>
1951                 <span class="keyword">if</span><span class="special">(</span><span class="identifier">known_units</span><span class="special">.</span><span class="identifier">find</span><span class="special">(</span><span class="identifier">input</span><span class="special">)</span> <span class="special">!=</span> <span class="identifier">known_units</span><span class="special">.</span><span class="identifier">end</span><span class="special">())</span>
1952                 <span class="special">{</span>
1953                     <span class="identifier">output_type</span> <span class="special">=</span> <span class="identifier">input</span><span class="special">;</span>
1954                     <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Done."</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1955                 <span class="special">}</span>
1956                 <span class="keyword">else</span>
1957                 <span class="special">{</span>
1958                     <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Unknown unit \""</span> <span class="special">&lt;&lt;</span> <span class="identifier">input</span> <span class="special">&lt;&lt;</span> <span class="string">"\""</span>
1959                          <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1960                 <span class="special">}</span>
1961             <span class="special">}</span>
1962             <span class="keyword">else</span>
1963             <span class="special">{</span>
1964                 <span class="keyword">break</span><span class="special">;</span>
1965             <span class="special">}</span>
1966         <span class="special">}</span>
1967         <span class="keyword">else</span>
1968         <span class="special">{</span>
1969             <span class="keyword">try</span>
1970             <span class="special">{</span>
1971                 <span class="keyword">double</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lexical_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span><span class="identifier">input</span><span class="special">);</span>
1972
1973                 <span class="keyword">if</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cin</span> <span class="special">&gt;&gt;</span> <span class="identifier">input</span><span class="special">)</span>
1974                 <span class="special">{</span>
1975                     <span class="keyword">if</span><span class="special">(</span><span class="identifier">known_units</span><span class="special">.</span><span class="identifier">find</span><span class="special">(</span><span class="identifier">input</span><span class="special">)</span> <span class="special">!=</span> <span class="identifier">known_units</span><span class="special">.</span><span class="identifier">end</span><span class="special">())</span>
1976                     <span class="special">{</span>
1977                         <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(</span>
1978                             <span class="identifier">calculate</span><span class="special">(</span><span class="identifier">value</span> <span class="special">*</span> <span class="identifier">known_units</span><span class="special">[</span><span class="identifier">input</span><span class="special">])</span> <span class="special">/</span>
1979                             <span class="identifier">known_units</span><span class="special">[</span><span class="identifier">output_type</span><span class="special">])</span>
1980                             <span class="special">&lt;&lt;</span> <span class="char">' '</span> <span class="special">&lt;&lt;</span> <span class="identifier">output_type</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1981                     <span class="special">}</span>
1982                     <span class="keyword">else</span>
1983                     <span class="special">{</span>
1984                         <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Unknown unit \""</span> <span class="special">&lt;&lt;</span> <span class="identifier">input</span> <span class="special">&lt;&lt;</span> <span class="string">"\""</span>
1985                             <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1986                     <span class="special">}</span>
1987                 <span class="special">}</span>
1988                 <span class="keyword">else</span>
1989                 <span class="special">{</span>
1990                     <span class="keyword">break</span><span class="special">;</span>
1991                 <span class="special">}</span>
1992             <span class="special">}</span>
1993             <span class="keyword">catch</span><span class="special">(...)</span>
1994             <span class="special">{</span>
1995                 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Input error"</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
1996             <span class="special">}</span>
1997         <span class="special">}</span>
1998     <span class="special">}</span>
1999 <span class="special">}</span>
2000 </pre>
2001 <p>
2002       </p>
2003 </div>
2004 <div class="section">
2005 <div class="titlepage"><div><div><h3 class="title">
2006 <a name="boost_units.Examples.lambda"></a><a class="link" href="Examples.html#boost_units.Examples.lambda" title="Interoperability with Boost.Lambda">Interoperability with Boost.Lambda</a>
2007 </h3></div></div></div>
2008 <p>
2009         (<a href="../../../libs/units/example/lambda.cpp" target="_top">lambda.cpp</a>)
2010       </p>
2011 <p>
2012         The header <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.lambda_hpp" title="Header &lt;boost/units/lambda.hpp&gt;">boost/units/lambda.hpp</a></code>
2013         provides overloads and specializations needed to make Boost.Units usable
2014         with the Boost.Lambda library.
2015       </p>
2016 <p>
2017 </p>
2018 <pre class="programlisting"><span class="keyword">int</span> <span class="identifier">main</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">argc</span><span class="special">,</span> <span class="keyword">char</span> <span class="special">**</span><span class="identifier">argv</span><span class="special">)</span> <span class="special">{</span>
2019
2020    <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">std</span><span class="special">;</span>
2021    <span class="keyword">namespace</span> <span class="identifier">bl</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lambda</span><span class="special">;</span>
2022    <span class="keyword">namespace</span> <span class="identifier">bu</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">;</span>
2023    <span class="keyword">namespace</span> <span class="identifier">si</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">units</span><span class="special">::</span><span class="identifier">si</span><span class="special">;</span>
2024
2025
2026    <span class="comment">////////////////////////////////////////////////////////////////////////</span>
2027    <span class="comment">// Mechanical example: linear accelerated movement</span>
2028    <span class="comment">////////////////////////////////////////////////////////////////////////</span>
2029
2030    <span class="comment">// Initial condition variables for acceleration, speed, and displacement</span>
2031    <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">acceleration</span><span class="special">&gt;</span> <span class="identifier">a</span> <span class="special">=</span> <span class="number">2.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meters_per_second_squared</span><span class="special">;</span>
2032    <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">velocity</span><span class="special">&gt;</span> <span class="identifier">v</span> <span class="special">=</span> <span class="number">1.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meters_per_second</span><span class="special">;</span>
2033    <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="identifier">s0</span> <span class="special">=</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">;</span>
2034
2035    <span class="comment">// Displacement over time</span>
2036    <span class="identifier">boost</span><span class="special">::</span><span class="identifier">function</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="special">(</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">time</span><span class="special">&gt;)</span> <span class="special">&gt;</span>
2037        <span class="identifier">s</span> <span class="special">=</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">var</span><span class="special">(</span><span class="identifier">a</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">_1</span> <span class="special">*</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">_1</span>
2038            <span class="special">+</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">var</span><span class="special">(</span><span class="identifier">v</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">_1</span>
2039            <span class="special">+</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">var</span><span class="special">(</span><span class="identifier">s0</span><span class="special">);</span>
2040
2041    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Linear accelerated movement:"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2042         <span class="special">&lt;&lt;</span> <span class="string">"a = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">a</span> <span class="special">&lt;&lt;</span> <span class="string">", v = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">v</span> <span class="special">&lt;&lt;</span> <span class="string">", s0 = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">s0</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2043         <span class="special">&lt;&lt;</span> <span class="string">"s(1.0 * si::second) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">s</span><span class="special">(</span><span class="number">1.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2044         <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
2045
2046    <span class="comment">// Change initial conditions</span>
2047    <span class="identifier">a</span> <span class="special">=</span> <span class="number">1.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meters_per_second_squared</span><span class="special">;</span>
2048    <span class="identifier">v</span> <span class="special">=</span> <span class="number">2.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meters_per_second</span><span class="special">;</span>
2049    <span class="identifier">s0</span> <span class="special">=</span> <span class="special">-</span><span class="number">1.5</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">;</span>
2050
2051    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"a = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">a</span> <span class="special">&lt;&lt;</span> <span class="string">", v = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">v</span> <span class="special">&lt;&lt;</span> <span class="string">", s0 = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">s0</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2052         <span class="special">&lt;&lt;</span> <span class="string">"s(1.0 * si::second) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">s</span><span class="special">(</span><span class="number">1.0</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2053         <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
2054
2055
2056    <span class="comment">////////////////////////////////////////////////////////////////////////</span>
2057    <span class="comment">// Electrical example: oscillating current</span>
2058    <span class="comment">////////////////////////////////////////////////////////////////////////</span>
2059
2060    <span class="comment">// Constants for the current amplitude, frequency, and offset current</span>
2061    <span class="keyword">const</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">current</span><span class="special">&gt;</span> <span class="identifier">iamp</span> <span class="special">=</span> <span class="number">1.5</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">ampere</span><span class="special">;</span>
2062    <span class="keyword">const</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">frequency</span><span class="special">&gt;</span> <span class="identifier">f</span> <span class="special">=</span> <span class="number">1.0e3</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">hertz</span><span class="special">;</span>
2063    <span class="keyword">const</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">current</span><span class="special">&gt;</span> <span class="identifier">i0</span> <span class="special">=</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">ampere</span><span class="special">;</span>
2064
2065    <span class="comment">// The invocation of the sin function needs to be postponed using</span>
2066    <span class="comment">// bind to specify the oscillation function. A lengthy static_cast</span>
2067    <span class="comment">// to the function pointer referencing boost::units::sin() is needed</span>
2068    <span class="comment">// to avoid an "unresolved overloaded function type" error.</span>
2069    <span class="identifier">boost</span><span class="special">::</span><span class="identifier">function</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">current</span><span class="special">&gt;</span> <span class="special">(</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">time</span><span class="special">&gt;)</span> <span class="special">&gt;</span>
2070        <span class="identifier">i</span> <span class="special">=</span> <span class="identifier">iamp</span>
2071            <span class="special">*</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">bind</span><span class="special">(</span><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">dimensionless_quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">system</span><span class="special">,</span> <span class="keyword">double</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="special">(*)(</span><span class="keyword">const</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">plane_angle</span><span class="special">&gt;&amp;)&gt;(</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">sin</span><span class="special">),</span>
2072                       <span class="number">2.0</span> <span class="special">*</span> <span class="identifier">pi</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">radian</span> <span class="special">*</span> <span class="identifier">f</span> <span class="special">*</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">_1</span><span class="special">)</span>
2073            <span class="special">+</span> <span class="identifier">i0</span><span class="special">;</span>
2074
2075    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Oscillating current:"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2076         <span class="special">&lt;&lt;</span> <span class="string">"iamp = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">iamp</span> <span class="special">&lt;&lt;</span> <span class="string">", f = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">f</span> <span class="special">&lt;&lt;</span> <span class="string">", i0 = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">i0</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2077         <span class="special">&lt;&lt;</span> <span class="string">"i(1.25e-3 * si::second) = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">i</span><span class="special">(</span><span class="number">1.25e-3</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">second</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2078         <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
2079
2080
2081    <span class="comment">////////////////////////////////////////////////////////////////////////</span>
2082    <span class="comment">// Geometric example: area calculation for a square</span>
2083    <span class="comment">////////////////////////////////////////////////////////////////////////</span>
2084
2085    <span class="comment">// Length constant</span>
2086    <span class="keyword">const</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;</span> <span class="identifier">l</span> <span class="special">=</span> <span class="number">1.5</span> <span class="special">*</span> <span class="identifier">si</span><span class="special">::</span><span class="identifier">meter</span><span class="special">;</span>
2087
2088    <span class="comment">// Again an ugly static_cast is needed to bind pow&lt;2&gt; to the first</span>
2089    <span class="comment">// function argument.</span>
2090    <span class="identifier">boost</span><span class="special">::</span><span class="identifier">function</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">area</span><span class="special">&gt;</span> <span class="special">(</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;)</span> <span class="special">&gt;</span>
2091        <span class="identifier">A</span> <span class="special">=</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">bind</span><span class="special">(</span><span class="keyword">static_cast</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">area</span><span class="special">&gt;</span> <span class="special">(*)(</span><span class="keyword">const</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">length</span><span class="special">&gt;&amp;)&gt;(</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">pow</span><span class="special">&lt;</span><span class="number">2</span><span class="special">&gt;),</span>
2092                     <span class="identifier">bl</span><span class="special">::</span><span class="identifier">_1</span><span class="special">);</span>
2093
2094    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Area of a square:"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2095         <span class="special">&lt;&lt;</span> <span class="string">"A("</span> <span class="special">&lt;&lt;</span> <span class="identifier">l</span> <span class="special">&lt;&lt;</span><span class="string">") = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">A</span><span class="special">(</span><span class="identifier">l</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
2096
2097
2098    <span class="comment">////////////////////////////////////////////////////////////////////////</span>
2099    <span class="comment">// Thermal example: temperature difference of two absolute temperatures</span>
2100    <span class="comment">////////////////////////////////////////////////////////////////////////</span>
2101
2102    <span class="comment">// Absolute temperature constants</span>
2103    <span class="keyword">const</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">absolute</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;</span> <span class="special">&gt;</span>
2104        <span class="identifier">Tref</span> <span class="special">=</span> <span class="number">273.15</span> <span class="special">*</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">absolute</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;();</span>
2105    <span class="keyword">const</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">absolute</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;</span> <span class="special">&gt;</span>
2106        <span class="identifier">Tamb</span> <span class="special">=</span> <span class="number">300.00</span> <span class="special">*</span> <span class="identifier">bu</span><span class="special">::</span><span class="identifier">absolute</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;();</span>
2107
2108    <span class="identifier">boost</span><span class="special">::</span><span class="identifier">function</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;</span> <span class="special">(</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">absolute</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;</span> <span class="special">&gt;,</span>
2109                                                   <span class="identifier">bu</span><span class="special">::</span><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">bu</span><span class="special">::</span><span class="identifier">absolute</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">temperature</span><span class="special">&gt;</span> <span class="special">&gt;)&gt;</span>
2110        <span class="identifier">dT</span> <span class="special">=</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">_2</span> <span class="special">-</span> <span class="identifier">bl</span><span class="special">::</span><span class="identifier">_1</span><span class="special">;</span>
2111
2112    <span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="string">"Temperature difference of two absolute temperatures:"</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2113         <span class="special">&lt;&lt;</span> <span class="string">"dT("</span> <span class="special">&lt;&lt;</span> <span class="identifier">Tref</span> <span class="special">&lt;&lt;</span> <span class="string">", "</span> <span class="special">&lt;&lt;</span> <span class="identifier">Tamb</span> <span class="special">&lt;&lt;</span> <span class="string">") = "</span> <span class="special">&lt;&lt;</span> <span class="identifier">dT</span><span class="special">(</span><span class="identifier">Tref</span><span class="special">,</span> <span class="identifier">Tamb</span><span class="special">)</span> <span class="special">&lt;&lt;</span> <span class="identifier">endl</span>
2114         <span class="special">&lt;&lt;</span> <span class="identifier">endl</span><span class="special">;</span>
2115
2116
2117    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
2118 <span class="special">}</span>
2119 </pre>
2120 <p>
2121       </p>
2122 </div>
2123 </div>
2124 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
2125 <td align="left"></td>
2126 <td align="right"><div class="copyright-footer">Copyright &#169; 2003-2008 Matthias Christian Schabel<br>Copyright &#169; 2007-2010 Steven
2127       Watanabe<p>
2128         Distributed under the Boost Software License, Version 1.0. (See accompanying
2129         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>)
2130       </p>
2131 </div></td>
2132 </tr></table>
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