ceph/src/boost/libs/mpl/doc/tutorial/representing-dimensions.html

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  10 <title>THE BOOST MPL LIBRARY: Representing Dimensions</title>
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  17 <div class="section" id="representing-dimensions">
  18 <h1><a class="toc-backref" href="./dimensional-analysis.html#id42" name="representing-dimensions">Representing Dimensions</a></h1>
  19 <p>An international standard called <em>Système
  20 International d'Unites</em> (SI), breaks every quantity down into a
  21 combination of the dimensions <em>mass</em>, <em>length</em> (or <em>position</em>),
  22 <em>time</em>, <em>charge</em>, <em>temperature</em>, <em>intensity</em>, and <em>angle</em>.  To be
  23 reasonably general, our system would have to be able to
  24 represent seven or more fundamental dimensions.  It also needs
  25 the ability to represent composite dimensions that, like <em>force</em>,
  26 are built through multiplication or division of the fundamental
  27 ones.</p>
  28 <p>In general, a composite dimension is the product of powers of
  29 fundamental dimensions. <a class="footnote-reference" href="#divisor" id="id6" name="id6">[1]</a>  If we were going to represent
  30 these powers for manipulation at runtime, we could use an array of
  31 seven <tt class="literal"><span class="pre">int</span></tt>s, with each position in the array holding the power
  32 of a different fundamental dimension:</p>
  33 <pre class="literal-block">
  34 typedef int dimension[7]; // m  l  t  ...
  35 dimension const mass      = {1, 0, 0, 0, 0, 0, 0};
  36 dimension const length    = {0, 1, 0, 0, 0, 0, 0};
  37 dimension const time      = {0, 0, 1, 0, 0, 0, 0};
  38 ...
  39 </pre>
  40 <table class="footnote" frame="void" id="divisor" rules="none">
  41 <colgroup><col class="label" /><col /></colgroup>
  42 <tbody valign="top">
  43 <tr><td class="label"><a class="fn-backref" href="#id6" name="divisor">[1]</a></td><td>Divisors just contribute negative exponents, since
  44 1/<em>x</em> = <em>x</em><sup>-1</sup>.</td></tr>
  45 </tbody>
  46 </table>
  47 <p>In that representation, force would be:</p>
  48 <pre class="literal-block">
  49 dimension const force  = {1, 1, -2, 0, 0, 0, 0};
  50 </pre>
  51 <!-- @compile(2) -->
  52 <!-- @litre_translator.line_offset -= 7 -->
  53 <p>that is, <em>mlt</em><sup>-2</sup>.  However, if we want to get dimensions into the
  54 type system, these arrays won't do the trick: they're all
  55 the same type!  Instead, we need types that <em>themselves</em> represent
  56 sequences of numbers, so that two masses have the same type and a
  57 mass is a different type from a length.</p>
  58 <p>Fortunately, the MPL provides us with a collection of <strong>type
  59 sequences</strong>.  For example, we can build a sequence of the built-in
  60 signed integral types this way:</p>
  61 <pre class="literal-block">
  62 #include &lt;boost/mpl/vector.hpp&gt;
  63
  64 typedef boost::mpl::vector&lt;
  65      signed char, short, int, long&gt; signed_types;
  66 </pre>
  67 <p>How can we use a type sequence to represent numbers?  Just as
  68 numerical metafunctions pass and return wrapper <em>types</em> having a
  69 nested <tt class="literal"><span class="pre">::value</span></tt>, so numerical sequences are really sequences of
  70 wrapper types (another example of polymorphism).  To make this sort
  71 of thing easier, MPL supplies the <tt class="literal"><span class="pre">int_&lt;N&gt;</span></tt> class template, which
  72 presents its integral argument as a nested <tt class="literal"><span class="pre">::value</span></tt>:</p>
  73 <pre class="literal-block">
  74 #include &lt;boost/mpl/int.hpp&gt;
  75
  76 namespace mpl = boost::mpl; // namespace alias
  77 static int const five = mpl::int_&lt;5&gt;::value;
  78 </pre>
  79 <div class="sidebar">
  80 <p class="sidebar-title first">Namespace Aliases</p>
  81 <div class="line-block">
  82 <div class="line"><tt class="literal"><span class="pre">namespace</span></tt> <em>alias</em> <tt class="literal"><span class="pre">=</span></tt> <em>namespace-name</em><tt class="literal"><span class="pre">;</span></tt></div>
  83 </div>
  84 <p>declares <em>alias</em> to be a synonym for <em>namespace-name</em>.  Many
  85 examples in this book will use <tt class="literal"><span class="pre">mpl::</span></tt> to indicate
  86 <tt class="literal"><span class="pre">boost::mpl::</span></tt>, but will omit the alias that makes it legal
  87 C++.</p>
  88 </div>
  89 <!-- @ignore() # nonsense isn't worth testing
  90 prefix +=['''
  91     #include <boost/mpl/int.hpp>
  92     #include <boost/mpl/vector.hpp>
  93 '''] -->
  94 <p>In fact, the library contains a whole suite of integral constant
  95 wrappers such as <tt class="literal"><span class="pre">long_</span></tt> and <tt class="literal"><span class="pre">bool_</span></tt>, each one wrapping a
  96 different type of integral constant within a class template.</p>
  97 <p>Now we can build our fundamental dimensions:</p>
  98 <pre class="literal-block">
  99 typedef mpl::vector&lt;
 100    mpl::int_&lt;1&gt;, mpl::int_&lt;0&gt;, mpl::int_&lt;0&gt;, mpl::int_&lt;0&gt;
 101  , mpl::int_&lt;0&gt;, mpl::int_&lt;0&gt;, mpl::int_&lt;0&gt;
 102 &gt; mass;
 103
 104 typedef mpl::vector&lt;
 105    mpl::int_&lt;0&gt;, mpl::int_&lt;1&gt;, mpl::int_&lt;0&gt;, mpl::int_&lt;0&gt;
 106  , mpl::int_&lt;0&gt;, mpl::int_&lt;0&gt;, mpl::int_&lt;0&gt;
 107 &gt; length;
 108 ...
 109 </pre>
 110 <!-- @ # We explained about the implicit namespace alias above
 111 prefix.append("""
 112 namespace boost{namespace mpl {}}
 113 namespace mpl = boost::mpl;
 114 """)
 115 compile('all') -->
 116 <p>Whew!  That's going to get tiring pretty quickly.  Worse, it's hard
 117 to read and verify:  The essential information, the powers of each
 118 fundamental dimension, is buried in repetitive syntactic &quot;noise.&quot;
 119 Accordingly, MPL supplies <strong>integral sequence wrappers</strong> that allow
 120 us to write:</p>
 121 <pre class="literal-block">
 122 #include &lt;boost/mpl/vector_c.hpp&gt;
 123
 124 typedef mpl::vector_c&lt;int,1,0,0,0,0,0,0&gt; mass;
 125 typedef mpl::vector_c&lt;int,0,1,0,0,0,0,0&gt; length; // or position
 126 typedef mpl::vector_c&lt;int,0,0,1,0,0,0,0&gt; time;
 127 typedef mpl::vector_c&lt;int,0,0,0,1,0,0,0&gt; charge;
 128 typedef mpl::vector_c&lt;int,0,0,0,0,1,0,0&gt; temperature;
 129 typedef mpl::vector_c&lt;int,0,0,0,0,0,1,0&gt; intensity;
 130 typedef mpl::vector_c&lt;int,0,0,0,0,0,0,1&gt; angle;
 131 </pre>
 132 <p>Even though they have different types, you can think of these
 133 <tt class="literal"><span class="pre">mpl::vector_c</span></tt> specializations as being equivalent to the more
 134 verbose versions above that use <tt class="literal"><span class="pre">mpl::vector</span></tt>.</p>
 135 <p>If we want, we can also define a few composite dimensions:</p>
 136 <pre class="literal-block">
 137 // base dimension:        m l  t ...
 138 typedef mpl::vector_c&lt;int,0,1,-1,0,0,0,0&gt; velocity;     // l/t
 139 typedef mpl::vector_c&lt;int,0,1,-2,0,0,0,0&gt; acceleration; // l/(t<sup>2</sup>)
 140 typedef mpl::vector_c&lt;int,1,1,-1,0,0,0,0&gt; momentum;     // ml/t
 141 typedef mpl::vector_c&lt;int,1,1,-2,0,0,0,0&gt; force;        // ml/(t<sup>2</sup>)
 142 </pre>
 143 <p>And, incidentally, the dimensions of scalars (like pi) can be
 144 described as:</p>
 145 <pre class="literal-block">
 146 typedef mpl::vector_c&lt;int,0,0,0,0,0,0,0&gt; scalar;
 147 </pre>
 148 <!-- @stack[0].replace('hpp>', 'hpp>\nnamespace {')
 149 stack[0].append('}')
 150 compile('all', pop = None) -->
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