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157 lines
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<!-- Copyright Aleksey Gurtovoy 2006. Distributed under the Boost -->
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<title>THE BOOST MPL LIBRARY: Representing Dimensions</title>
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<table class="header"><tr class="header"><td class="header-group navigation-bar"><span class="navigation-group"><a href="./dimensional-analysis.html" class="navigation-link">Prev</a> <a href="./representing-quantities.html" class="navigation-link">Next</a></span><span class="navigation-group-separator"> | </span><span class="navigation-group">Back <a href="./representing-quantities.html" class="navigation-link">Along</a></span><span class="navigation-group-separator"> | </span><span class="navigation-group"><a href="./dimensional-analysis.html" class="navigation-link">Up</a> <a href="../index.html" class="navigation-link">Home</a></span><span class="navigation-group-separator"> | </span><span class="navigation-group"><a href="./tutorial_toc.html" class="navigation-link">Full TOC</a></span></td>
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<td class="header-group page-location"><a href="../index.html" class="navigation-link">Front Page</a> / <a href="./tutorial-metafunctions.html" class="navigation-link">Tutorial: Metafunctions and Higher-Order Metaprogramming</a> / <a href="./dimensional-analysis.html" class="navigation-link">Dimensional Analysis</a> / <a href="./representing-dimensions.html" class="navigation-link">Representing Dimensions</a></td>
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</tr></table><div class="header-separator"></div>
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<div class="section" id="representing-dimensions">
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<h1><a class="toc-backref" href="./dimensional-analysis.html#id42" name="representing-dimensions">Representing Dimensions</a></h1>
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<p>An international standard called <em>Système
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International d'Unites</em> (SI), breaks every quantity down into a
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combination of the dimensions <em>mass</em>, <em>length</em> (or <em>position</em>),
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<em>time</em>, <em>charge</em>, <em>temperature</em>, <em>intensity</em>, and <em>angle</em>. To be
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reasonably general, our system would have to be able to
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represent seven or more fundamental dimensions. It also needs
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the ability to represent composite dimensions that, like <em>force</em>,
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are built through multiplication or division of the fundamental
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ones.</p>
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<p>In general, a composite dimension is the product of powers of
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fundamental dimensions. <a class="footnote-reference" href="#divisor" id="id6" name="id6">[1]</a> If we were going to represent
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these powers for manipulation at runtime, we could use an array of
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seven <tt class="literal"><span class="pre">int</span></tt>s, with each position in the array holding the power
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of a different fundamental dimension:</p>
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<pre class="literal-block">
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typedef int dimension[7]; // m l t ...
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dimension const mass = {1, 0, 0, 0, 0, 0, 0};
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dimension const length = {0, 1, 0, 0, 0, 0, 0};
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dimension const time = {0, 0, 1, 0, 0, 0, 0};
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...
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</pre>
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<table class="footnote" frame="void" id="divisor" rules="none">
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<colgroup><col class="label" /><col /></colgroup>
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<tbody valign="top">
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<tr><td class="label"><a class="fn-backref" href="#id6" name="divisor">[1]</a></td><td>Divisors just contribute negative exponents, since
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1/<em>x</em> = <em>x</em><sup>-1</sup>.</td></tr>
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</tbody>
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</table>
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<p>In that representation, force would be:</p>
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<pre class="literal-block">
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dimension const force = {1, 1, -2, 0, 0, 0, 0};
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</pre>
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<!-- @compile(2) -->
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<!-- @litre_translator.line_offset -= 7 -->
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<p>that is, <em>mlt</em><sup>-2</sup>. However, if we want to get dimensions into the
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type system, these arrays won't do the trick: they're all
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the same type! Instead, we need types that <em>themselves</em> represent
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sequences of numbers, so that two masses have the same type and a
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mass is a different type from a length.</p>
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<p>Fortunately, the MPL provides us with a collection of <strong>type
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sequences</strong>. For example, we can build a sequence of the built-in
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signed integral types this way:</p>
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<pre class="literal-block">
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#include <boost/mpl/vector.hpp>
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typedef boost::mpl::vector<
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signed char, short, int, long> signed_types;
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</pre>
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<p>How can we use a type sequence to represent numbers? Just as
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numerical metafunctions pass and return wrapper <em>types</em> having a
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nested <tt class="literal"><span class="pre">::value</span></tt>, so numerical sequences are really sequences of
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wrapper types (another example of polymorphism). To make this sort
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of thing easier, MPL supplies the <tt class="literal"><span class="pre">int_<N></span></tt> class template, which
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presents its integral argument as a nested <tt class="literal"><span class="pre">::value</span></tt>:</p>
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<pre class="literal-block">
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#include <boost/mpl/int.hpp>
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namespace mpl = boost::mpl; // namespace alias
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static int const five = mpl::int_<5>::value;
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</pre>
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<div class="sidebar">
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<p class="sidebar-title first">Namespace Aliases</p>
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<div class="line-block">
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<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>
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</div>
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<p>declares <em>alias</em> to be a synonym for <em>namespace-name</em>. Many
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examples in this book will use <tt class="literal"><span class="pre">mpl::</span></tt> to indicate
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<tt class="literal"><span class="pre">boost::mpl::</span></tt>, but will omit the alias that makes it legal
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C++.</p>
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</div>
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<!-- @ignore() # nonsense isn't worth testing
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prefix +=['''
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#include <boost/mpl/int.hpp>
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#include <boost/mpl/vector.hpp>
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'''] -->
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<p>In fact, the library contains a whole suite of integral constant
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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
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different type of integral constant within a class template.</p>
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<p>Now we can build our fundamental dimensions:</p>
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<pre class="literal-block">
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typedef mpl::vector<
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mpl::int_<1>, mpl::int_<0>, mpl::int_<0>, mpl::int_<0>
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, mpl::int_<0>, mpl::int_<0>, mpl::int_<0>
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> mass;
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typedef mpl::vector<
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mpl::int_<0>, mpl::int_<1>, mpl::int_<0>, mpl::int_<0>
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, mpl::int_<0>, mpl::int_<0>, mpl::int_<0>
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> length;
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...
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</pre>
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<!-- @ # We explained about the implicit namespace alias above
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prefix.append("""
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namespace boost{namespace mpl {}}
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namespace mpl = boost::mpl;
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""")
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compile('all') -->
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<p>Whew! That's going to get tiring pretty quickly. Worse, it's hard
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to read and verify: The essential information, the powers of each
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fundamental dimension, is buried in repetitive syntactic "noise."
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Accordingly, MPL supplies <strong>integral sequence wrappers</strong> that allow
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us to write:</p>
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<pre class="literal-block">
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#include <boost/mpl/vector_c.hpp>
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typedef mpl::vector_c<int,1,0,0,0,0,0,0> mass;
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typedef mpl::vector_c<int,0,1,0,0,0,0,0> length; // or position
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typedef mpl::vector_c<int,0,0,1,0,0,0,0> time;
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typedef mpl::vector_c<int,0,0,0,1,0,0,0> charge;
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typedef mpl::vector_c<int,0,0,0,0,1,0,0> temperature;
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typedef mpl::vector_c<int,0,0,0,0,0,1,0> intensity;
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typedef mpl::vector_c<int,0,0,0,0,0,0,1> angle;
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</pre>
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<p>Even though they have different types, you can think of these
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<tt class="literal"><span class="pre">mpl::vector_c</span></tt> specializations as being equivalent to the more
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verbose versions above that use <tt class="literal"><span class="pre">mpl::vector</span></tt>.</p>
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<p>If we want, we can also define a few composite dimensions:</p>
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<pre class="literal-block">
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// base dimension: m l t ...
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typedef mpl::vector_c<int,0,1,-1,0,0,0,0> velocity; // l/t
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typedef mpl::vector_c<int,0,1,-2,0,0,0,0> acceleration; // l/(t<sup>2</sup>)
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typedef mpl::vector_c<int,1,1,-1,0,0,0,0> momentum; // ml/t
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typedef mpl::vector_c<int,1,1,-2,0,0,0,0> force; // ml/(t<sup>2</sup>)
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</pre>
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<p>And, incidentally, the dimensions of scalars (like pi) can be
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described as:</p>
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<pre class="literal-block">
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typedef mpl::vector_c<int,0,0,0,0,0,0,0> scalar;
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</pre>
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<!-- @stack[0].replace('hpp>', 'hpp>\nnamespace {')
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stack[0].append('}')
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compile('all', pop = None) -->
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