<?xml version="1.0" encoding="utf-8" ?> <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> <!-- Copyright Aleksey Gurtovoy 2006. Distributed under the Boost --> <!-- Software License, Version 1.0. (See accompanying --> <!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) --> <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <meta name="generator" content="Docutils 0.3.6: http://docutils.sourceforge.net/" /> <title>THE BOOST MPL LIBRARY: Representing Dimensions</title> <link rel="stylesheet" href="../style.css" type="text/css" /> </head> <body class="docframe"> <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> <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> </tr></table><div class="header-separator"></div> <div class="section" id="representing-dimensions"> <h1><a class="toc-backref" href="./dimensional-analysis.html#id42" name="representing-dimensions">Representing Dimensions</a></h1> <p>An international standard called <em>Système International d'Unites</em> (SI), breaks every quantity down into a combination of the dimensions <em>mass</em>, <em>length</em> (or <em>position</em>), <em>time</em>, <em>charge</em>, <em>temperature</em>, <em>intensity</em>, and <em>angle</em>. To be reasonably general, our system would have to be able to represent seven or more fundamental dimensions. It also needs the ability to represent composite dimensions that, like <em>force</em>, are built through multiplication or division of the fundamental ones.</p> <p>In general, a composite dimension is the product of powers of fundamental dimensions. <a class="footnote-reference" href="#divisor" id="id6" name="id6">[1]</a> If we were going to represent these powers for manipulation at runtime, we could use an array of seven <tt class="literal"><span class="pre">int</span></tt>s, with each position in the array holding the power of a different fundamental dimension:</p> <pre class="literal-block"> typedef int dimension[7]; // m l t ... dimension const mass = {1, 0, 0, 0, 0, 0, 0}; dimension const length = {0, 1, 0, 0, 0, 0, 0}; dimension const time = {0, 0, 1, 0, 0, 0, 0}; ... </pre> <table class="footnote" frame="void" id="divisor" rules="none"> <colgroup><col class="label" /><col /></colgroup> <tbody valign="top"> <tr><td class="label"><a class="fn-backref" href="#id6" name="divisor">[1]</a></td><td>Divisors just contribute negative exponents, since 1/<em>x</em> = <em>x</em><sup>-1</sup>.</td></tr> </tbody> </table> <p>In that representation, force would be:</p> <pre class="literal-block"> dimension const force = {1, 1, -2, 0, 0, 0, 0}; </pre> <!-- @compile(2) --> <!-- @litre_translator.line_offset -= 7 --> <p>that is, <em>mlt</em><sup>-2</sup>. However, if we want to get dimensions into the type system, these arrays won't do the trick: they're all the same type! Instead, we need types that <em>themselves</em> represent sequences of numbers, so that two masses have the same type and a mass is a different type from a length.</p> <p>Fortunately, the MPL provides us with a collection of <strong>type sequences</strong>. For example, we can build a sequence of the built-in signed integral types this way:</p> <pre class="literal-block"> #include <boost/mpl/vector.hpp> typedef boost::mpl::vector< signed char, short, int, long> signed_types; </pre> <p>How can we use a type sequence to represent numbers? Just as numerical metafunctions pass and return wrapper <em>types</em> having a nested <tt class="literal"><span class="pre">::value</span></tt>, so numerical sequences are really sequences of wrapper types (another example of polymorphism). To make this sort of thing easier, MPL supplies the <tt class="literal"><span class="pre">int_<N></span></tt> class template, which presents its integral argument as a nested <tt class="literal"><span class="pre">::value</span></tt>:</p> <pre class="literal-block"> #include <boost/mpl/int.hpp> namespace mpl = boost::mpl; // namespace alias static int const five = mpl::int_<5>::value; </pre> <div class="sidebar"> <p class="sidebar-title first">Namespace Aliases</p> <div class="line-block"> <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> </div> <p>declares <em>alias</em> to be a synonym for <em>namespace-name</em>. Many examples in this book will use <tt class="literal"><span class="pre">mpl::</span></tt> to indicate <tt class="literal"><span class="pre">boost::mpl::</span></tt>, but will omit the alias that makes it legal C++.</p> </div> <!-- @ignore() # nonsense isn't worth testing prefix +=[''' #include <boost/mpl/int.hpp> #include <boost/mpl/vector.hpp> '''] --> <p>In fact, the library contains a whole suite of integral constant 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 different type of integral constant within a class template.</p> <p>Now we can build our fundamental dimensions:</p> <pre class="literal-block"> typedef mpl::vector< mpl::int_<1>, mpl::int_<0>, mpl::int_<0>, mpl::int_<0> , mpl::int_<0>, mpl::int_<0>, mpl::int_<0> > mass; typedef mpl::vector< mpl::int_<0>, mpl::int_<1>, mpl::int_<0>, mpl::int_<0> , mpl::int_<0>, mpl::int_<0>, mpl::int_<0> > length; ... </pre> <!-- @ # We explained about the implicit namespace alias above prefix.append(""" namespace boost{namespace mpl {}} namespace mpl = boost::mpl; """) compile('all') --> <p>Whew! That's going to get tiring pretty quickly. Worse, it's hard to read and verify: The essential information, the powers of each fundamental dimension, is buried in repetitive syntactic "noise." Accordingly, MPL supplies <strong>integral sequence wrappers</strong> that allow us to write:</p> <pre class="literal-block"> #include <boost/mpl/vector_c.hpp> typedef mpl::vector_c<int,1,0,0,0,0,0,0> mass; typedef mpl::vector_c<int,0,1,0,0,0,0,0> length; // or position typedef mpl::vector_c<int,0,0,1,0,0,0,0> time; typedef mpl::vector_c<int,0,0,0,1,0,0,0> charge; typedef mpl::vector_c<int,0,0,0,0,1,0,0> temperature; typedef mpl::vector_c<int,0,0,0,0,0,1,0> intensity; typedef mpl::vector_c<int,0,0,0,0,0,0,1> angle; </pre> <p>Even though they have different types, you can think of these <tt class="literal"><span class="pre">mpl::vector_c</span></tt> specializations as being equivalent to the more verbose versions above that use <tt class="literal"><span class="pre">mpl::vector</span></tt>.</p> <p>If we want, we can also define a few composite dimensions:</p> <pre class="literal-block"> // base dimension: m l t ... typedef mpl::vector_c<int,0,1,-1,0,0,0,0> velocity; // l/t typedef mpl::vector_c<int,0,1,-2,0,0,0,0> acceleration; // l/(t<sup>2</sup>) typedef mpl::vector_c<int,1,1,-1,0,0,0,0> momentum; // ml/t typedef mpl::vector_c<int,1,1,-2,0,0,0,0> force; // ml/(t<sup>2</sup>) </pre> <p>And, incidentally, the dimensions of scalars (like pi) can be described as:</p> <pre class="literal-block"> typedef mpl::vector_c<int,0,0,0,0,0,0,0> scalar; </pre> <!-- @stack[0].replace('hpp>', 'hpp>\nnamespace {') stack[0].append('}') compile('all', pop = None) --> </div> <div class="footer-separator"></div> <table class="footer"><tr class="footer"><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> </tr></table></body> </html>