doc/html/boost_units/Units.html

   1 <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
   2 <html>
   3 <head>
   4 <meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
   5 <title>Units</title>
   6 <link rel="stylesheet" href="../../../doc/src/boostbook.css" type="text/css">
   7 <meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
   8 <link rel="home" href="../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset">
   9 <link rel="up" href="../boost_units.html" title="Chapter&#160;43.&#160;Boost.Units 1.1.0">
  10 <link rel="prev" href="Dimensional_Analysis.html" title="Dimensional Analysis">
  11 <link rel="next" href="Quantities.html" title="Quantities">
  12 </head>
  13 <body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
  14 <table cellpadding="2" width="100%"><tr>
  15 <td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../boost.png"></td>
  16 <td align="center"><a href="../../../index.html">Home</a></td>
  17 <td align="center"><a href="../../../libs/libraries.htm">Libraries</a></td>
  18 <td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
  19 <td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
  20 <td align="center"><a href="../../../more/index.htm">More</a></td>
  21 </tr></table>
  22 <hr>
  23 <div class="spirit-nav">
  24 <a accesskey="p" href="Dimensional_Analysis.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../boost_units.html"><img src="../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="Quantities.html"><img src="../../../doc/src/images/next.png" alt="Next"></a>
  25 </div>
  26 <div class="section">
  27 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  28 <a name="boost_units.Units"></a><a class="link" href="Units.html" title="Units">Units</a>
  29 </h2></div></div></div>
  30 <div class="toc"><dl class="toc">
  31 <dt><span class="section"><a href="Units.html#boost_units.Units.base_units">Base Units</a></span></dt>
  32 <dt><span class="section"><a href="Units.html#boost_units.Units.scaled_base_units">Scaled Base Units</a></span></dt>
  33 <dt><span class="section"><a href="Units.html#boost_units.Units.scaled_units">Scaled Units</a></span></dt>
  34 </dl></div>
  35 <p>
  36       We define a <span class="bold"><strong>unit</strong></span> as a set of base units each
  37       of which can be raised to an arbitrary rational exponent. Thus, the SI unit
  38       corresponding to the dimension of force is kg m s^-2, where kg, m, and s are
  39       base units. We use the notion of a <span class="bold"><strong>unit system</strong></span>
  40       such as SI to specify the mapping from a dimension to a particular unit so
  41       that instead of specifying the base units explicitly, we can just ask for the
  42       representation of a dimension in a particular system.
  43     </p>
  44 <p>
  45       Units are, like dimensions, purely compile-time variables with no associated
  46       value. Units obey the same algebra as dimensions do; the presence of the unit
  47       system serves to ensure that units having identical reduced dimension in different
  48       systems (like feet and meters) cannot be inadvertently mixed in computations.
  49     </p>
  50 <p>
  51       There are two distinct types of systems that can be envisioned:
  52     </p>
  53 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
  54 <li class="listitem">
  55           <span class="bold"><strong>Homogeneous systems</strong></span> : Systems which hold
  56           a linearly independent set of base units which can be used to represent
  57           many different dimensions. For example, the SI system has seven base dimensions
  58           and seven base units corresponding to them. It can represent any unit which
  59           uses only those seven base dimensions. Thus it is a homogeneous_system.
  60         </li>
  61 <li class="listitem">
  62           <span class="bold"><strong>Heterogeneous systems</strong></span> : Systems which
  63           store the exponents of every base unit involved are termed heterogeneous.
  64           Some units can only be represented in this way. For example, area in m
  65           ft is intrinsically heterogeneous, because the base units of meters and
  66           feet have identical dimensions. As a result, simply storing a dimension
  67           and a set of base units does not yield a unique solution. A practical example
  68           of the need for heterogeneous units, is an empirical equation used in aviation:
  69           H = (r/C)^2 where H is the radar beam height in feet and r is the radar
  70           range in nautical miles. In order to enforce dimensional correctness of
  71           this equation, the constant, C, must be expressed in nautical miles per
  72           foot^(1/2), mixing two distinct base units of length.
  73         </li>
  74 </ul></div>
  75 <p>
  76       Units are implemented by the <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/unit.html" title="Class template unit">unit</a></code></span>
  77       template class defined in <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.unit_hpp" title="Header &lt;boost/units/unit.hpp&gt;">boost/units/unit.hpp</a></code>
  78       :
  79     </p>
  80 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Dim</span><span class="special">,</span><span class="keyword">class</span> <span class="identifier">System</span><span class="special">&gt;</span> <span class="keyword">class</span> <span class="identifier">unit</span><span class="special">;</span>
  81 </pre>
  82 <p>
  83       In addition to supporting the compile-time dimensional analysis operations,
  84       the +, -, *, and / runtime operators are provided for <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/unit.html" title="Class template unit">unit</a></code></span> variables. Because the
  85       dimension associated with powers and roots must be computed at compile-time,
  86       it is not possible to provide overloads for <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">pow</span></code> that
  87       function correctly for <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/unit.html" title="Class template unit">unit</a></code></span>s.
  88       These operations are supported through free functions <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/pow_idp769329696.html" title="Function template pow">pow</a></code></span> and <span class="underline"><code class="computeroutput"><a class="link" href="Reference.html#boost.units.root_idp770184864">root</a></code></span> that are templated
  89       on integer and <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/static_rational.html" title="Class template static_rational">static_rational</a></code></span>
  90       values and can take as an argument any type for which the utility classes
  91       <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>
  92       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>
  93       have been defined.
  94     </p>
  95 <div class="section">
  96 <div class="titlepage"><div><div><h3 class="title">
  97 <a name="boost_units.Units.base_units"></a><a class="link" href="Units.html#boost_units.Units.base_units" title="Base Units">Base Units</a>
  98 </h3></div></div></div>
  99 <p>
 100         Base units are defined much like base dimensions.
 101       </p>
 102 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">Derived</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">Dimensions</span><span class="special">,</span> <span class="keyword">long</span> <span class="identifier">N</span><span class="special">&gt;</span> <span class="keyword">struct</span> <span class="identifier">base_unit</span> <span class="special">{</span> <span class="special">...</span> <span class="special">};</span>
 103 </pre>
 104 <p>
 105         Again negative ordinals are reserved.
 106       </p>
 107 <p>
 108         As an example, in the following we will implement a subset of the SI unit
 109         system based on the fundamental dimensions given above, demonstrating all
 110         steps necessary for a completely functional system. First, we simply define
 111         a unit system that includes type definitions for commonly used units:
 112       </p>
 113 <p>
 114 </p>
 115 <pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">meter_base_unit</span> <span class="special">:</span> <span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">meter_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> <span class="special">{</span> <span class="special">};</span>
 116 <span class="keyword">struct</span> <span class="identifier">kilogram_base_unit</span> <span class="special">:</span> <span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">kilogram_base_unit</span><span class="special">,</span> <span class="identifier">mass_dimension</span><span class="special">,</span> <span class="number">2</span><span class="special">&gt;</span> <span class="special">{</span> <span class="special">};</span>
 117 <span class="keyword">struct</span> <span class="identifier">second_base_unit</span> <span class="special">:</span> <span class="identifier">base_unit</span><span class="special">&lt;</span><span class="identifier">second_base_unit</span><span class="special">,</span> <span class="identifier">time_dimension</span><span class="special">,</span> <span class="number">3</span><span class="special">&gt;</span> <span class="special">{</span> <span class="special">};</span>
 118
 119 <span class="keyword">typedef</span> <span class="identifier">make_system</span><span class="special">&lt;</span>
 120     <span class="identifier">meter_base_unit</span><span class="special">,</span>
 121     <span class="identifier">kilogram_base_unit</span><span class="special">,</span>
 122     <span class="identifier">second_base_unit</span><span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">mks_system</span><span class="special">;</span>
 123
 124 <span class="comment">/// unit typedefs</span>
 125 <span class="keyword">typedef</span> <span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">dimensionless_type</span><span class="special">,</span><span class="identifier">mks_system</span><span class="special">&gt;</span>      <span class="identifier">dimensionless</span><span class="special">;</span>
 126
 127 <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">mks_system</span><span class="special">&gt;</span>        <span class="identifier">length</span><span class="special">;</span>
 128 <span class="keyword">typedef</span> <span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">mass_dimension</span><span class="special">,</span><span class="identifier">mks_system</span><span class="special">&gt;</span>          <span class="identifier">mass</span><span class="special">;</span>
 129 <span class="keyword">typedef</span> <span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">time_dimension</span><span class="special">,</span><span class="identifier">mks_system</span><span class="special">&gt;</span>          <span class="identifier">time</span><span class="special">;</span>
 130
 131 <span class="keyword">typedef</span> <span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">area_dimension</span><span class="special">,</span><span class="identifier">mks_system</span><span class="special">&gt;</span>          <span class="identifier">area</span><span class="special">;</span>
 132 <span class="keyword">typedef</span> <span class="identifier">unit</span><span class="special">&lt;</span><span class="identifier">energy_dimension</span><span class="special">,</span><span class="identifier">mks_system</span><span class="special">&gt;</span>        <span class="identifier">energy</span><span class="special">;</span>
 133 </pre>
 134 <p>
 135       </p>
 136 <p>
 137         The macro <span class="underline"><code class="computeroutput"><a class="link" href="../BOOST_UNITS_STATIC_CONSTANT.html" title="Macro BOOST_UNITS_STATIC_CONSTANT">BOOST_UNITS_STATIC_CONSTANT</a></code></span>
 138         is provided in <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.static_constant_hpp" title="Header &lt;boost/units/static_constant.hpp&gt;">boost/units/static_constant.hpp</a></code>
 139         to facilitate ODR- and thread-safe constant definition in header files. We
 140         then define some constants for the supported units to simplify variable definitions:
 141       </p>
 142 <p>
 143 </p>
 144 <pre class="programlisting"><span class="comment">/// unit constants </span>
 145 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">meter</span><span class="special">,</span><span class="identifier">length</span><span class="special">);</span>
 146 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">meters</span><span class="special">,</span><span class="identifier">length</span><span class="special">);</span>
 147 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">kilogram</span><span class="special">,</span><span class="identifier">mass</span><span class="special">);</span>
 148 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">kilograms</span><span class="special">,</span><span class="identifier">mass</span><span class="special">);</span>
 149 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">second</span><span class="special">,</span><span class="identifier">time</span><span class="special">);</span>
 150 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">seconds</span><span class="special">,</span><span class="identifier">time</span><span class="special">);</span>
 151
 152 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">square_meter</span><span class="special">,</span><span class="identifier">area</span><span class="special">);</span>
 153 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">square_meters</span><span class="special">,</span><span class="identifier">area</span><span class="special">);</span>
 154 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">joule</span><span class="special">,</span><span class="identifier">energy</span><span class="special">);</span>
 155 <span class="identifier">BOOST_UNITS_STATIC_CONSTANT</span><span class="special">(</span><span class="identifier">joules</span><span class="special">,</span><span class="identifier">energy</span><span class="special">);</span>
 156 </pre>
 157 <p>
 158       </p>
 159 <p>
 160         If support for textual output of units is desired, we can also specialize
 161         the <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/base_unit_info.html" title="Struct template base_unit_info">base_unit_info</a></code></span>
 162         class for each fundamental dimension tag:
 163       </p>
 164 <p>
 165 </p>
 166 <pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">struct</span> <span class="identifier">base_unit_info</span><span class="special">&lt;</span><span class="identifier">test</span><span class="special">::</span><span class="identifier">meter_base_unit</span><span class="special">&gt;</span>
 167 <span class="special">{</span>
 168     <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">"meter"</span><span class="special">;</span> <span class="special">}</span>
 169     <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">"m"</span><span class="special">;</span> <span class="special">}</span>
 170 <span class="special">};</span>
 171 </pre>
 172 <p>
 173       </p>
 174 <p>
 175         and similarly for <code class="computeroutput"><span class="identifier">kilogram_base_unit</span></code>
 176         and <code class="computeroutput"><span class="identifier">second_base_unit</span></code>. A future
 177         version of the library will provide a more flexible system allowing for internationalization
 178         through a facet/locale-type mechanism. The <code class="computeroutput"><span class="identifier">name</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">symbol</span><span class="special">()</span></code> methods of <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/base_unit_info.html" title="Struct template base_unit_info">base_unit_info</a></code></span>
 179         provide full and short names for the base unit. With these definitions, we
 180         have the rudimentary beginnings of our unit system, which can be used to
 181         determine reduced dimensions for arbitrary unit calculations.
 182       </p>
 183 </div>
 184 <div class="section">
 185 <div class="titlepage"><div><div><h3 class="title">
 186 <a name="boost_units.Units.scaled_base_units"></a><a class="link" href="Units.html#boost_units.Units.scaled_base_units" title="Scaled Base Units">Scaled Base Units</a>
 187 </h3></div></div></div>
 188 <p>
 189         Now, it is also possible to define a base unit as being a multiple of another
 190         base unit. For example, the way that <code class="computeroutput"><span class="identifier">kilogram_base_unit</span></code>
 191         is actually defined by the library is along the following lines
 192       </p>
 193 <pre class="programlisting"><span class="keyword">struct</span> <span class="identifier">gram_base_unit</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">base_unit</span><span class="special">&lt;</span><span class="identifier">gram_base_unit</span><span class="special">,</span> <span class="identifier">mass_dimension</span><span class="special">,</span> <span class="number">1</span><span class="special">&gt;</span> <span class="special">{};</span>
 194 <span class="keyword">typedef</span> <span class="identifier">scaled_base_unit</span><span class="special">&lt;</span><span class="identifier">gram_base_unit</span><span class="special">,</span> <span class="identifier">scale</span><span class="special">&lt;</span><span class="number">10</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;</span><span class="number">3</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;</span> <span class="identifier">kilogram_base_unit</span><span class="special">;</span>
 195 </pre>
 196 <p>
 197         This basically defines a kilogram as being 10^3 times a gram.
 198       </p>
 199 <p>
 200         There are several advantages to this approach.
 201       </p>
 202 <div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
 203 <li class="listitem">
 204             It reflects the real meaning of these units better than treating them
 205             as independent units.
 206           </li>
 207 <li class="listitem">
 208             If a conversion is defined between grams or kilograms and some other
 209             units, it will automatically work for both kilograms and grams, with
 210             only one specialization.
 211           </li>
 212 <li class="listitem">
 213             Similarly, if the symbol for grams is defined as "g", then
 214             the symbol for kilograms will be "kg" without any extra effort.
 215           </li>
 216 </ul></div>
 217 </div>
 218 <div class="section">
 219 <div class="titlepage"><div><div><h3 class="title">
 220 <a name="boost_units.Units.scaled_units"></a><a class="link" href="Units.html#boost_units.Units.scaled_units" title="Scaled Units">Scaled Units</a>
 221 </h3></div></div></div>
 222 <p>
 223         We can also scale a <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/unit.html" title="Class template unit">unit</a></code></span>
 224         as a whole, rather than scaling the individual base units which comprise
 225         it. For this purpose, we use the metafunction <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/make_scaled_unit.html" title="Struct template make_scaled_unit">make_scaled_unit</a></code></span>.
 226         The main motivation for this feature is the metric prefixes defined in <code class="computeroutput"><a class="link" href="Reference.html#header.boost.units.systems.si.prefixes_hpp" title="Header &lt;boost/units/systems/si/prefixes.hpp&gt;">boost/units/systems/si/prefixes.hpp</a></code>.
 227       </p>
 228 <p>
 229         A simple example of its usage would be.
 230       </p>
 231 <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">make_scaled_unit</span><span class="special">&lt;</span><span class="identifier">si</span><span class="special">::</span><span class="identifier">time</span><span class="special">,</span> <span class="identifier">scale</span><span class="special">&lt;</span><span class="number">10</span><span class="special">,</span> <span class="identifier">static_rational</span><span class="special">&lt;-</span><span class="number">9</span><span class="special">&gt;</span> <span class="special">&gt;</span> <span class="special">&gt;::</span><span class="identifier">type</span> <span class="identifier">nanosecond</span><span class="special">;</span>
 232 </pre>
 233 <p>
 234         nanosecond is a specialization of <span class="underline"><code class="computeroutput"><a class="link" href="../boost/units/unit.html" title="Class template unit">unit</a></code></span>,
 235         and can be used in a quantity normally.
 236       </p>
 237 <pre class="programlisting"><span class="identifier">quantity</span><span class="special">&lt;</span><span class="identifier">nanosecond</span><span class="special">&gt;</span> <span class="identifier">t</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">seconds</span><span class="special">);</span>
 238 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">t</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>    <span class="comment">// prints 1e9 ns</span>
 239 </pre>
 240 </div>
 241 </div>
 242 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 243 <td align="left"></td>
 244 <td align="right"><div class="copyright-footer">Copyright &#169; 2003-2008 Matthias Christian Schabel<br>Copyright &#169; 2007-2010 Steven
 245       Watanabe<p>
 246         Distributed under the Boost Software License, Version 1.0. (See accompanying
 247         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>)
 248       </p>
 249 </div></td>
 250 </tr></table>
 251 <hr>
 252 <div class="spirit-nav">
 253 <a accesskey="p" href="Dimensional_Analysis.html"><img src="../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../boost_units.html"><img src="../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="Quantities.html"><img src="../../../doc/src/images/next.png" alt="Next"></a>
 254 </div>
 255 </body>
 256 </html>