<?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: Implementing Division</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="./implementing.html" class="navigation-link">Prev</a> <a href="./higher-order.html" class="navigation-link">Next</a></span><span class="navigation-group-separator"> | </span><span class="navigation-group"><a href="./implementing.html" class="navigation-link">Back</a> Along</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="./implementing-division.html" class="navigation-link">Implementing Division</a></td> </tr></table><div class="header-separator"></div> <div class="section" id="implementing-division"> <h1><a class="toc-backref" href="./dimensional-analysis.html#id46" name="implementing-division">Implementing Division</a></h1> <p>Division is similar to multiplication, but instead of adding exponents, we must subtract them. Rather than writing out a near duplicate of <tt class="literal"><span class="pre">plus_f</span></tt>, we can use the following trick to make <tt class="literal"><span class="pre">minus_f</span></tt> much simpler:</p> <pre class="literal-block"> struct minus_f { template <class T1, class T2> struct apply : mpl::minus<T1,T2> {}; }; </pre> <!-- @ # The following is OK because we showed how to get at mpl_plus prefix.append('#include <boost/mpl/minus.hpp>') compile(1) --> <p>Here <tt class="literal"><span class="pre">minus_f::apply</span></tt> uses inheritance to expose the nested <tt class="literal"><span class="pre">type</span></tt> of its base class, <tt class="literal"><span class="pre">mpl::minus</span></tt>, so we don't have to write:</p> <pre class="literal-block"> typedef typename ...::type type </pre> <!-- @ignore() --> <p>We don't have to write <tt class="literal"><span class="pre">typename</span></tt> here (in fact, it would be illegal), because the compiler knows that dependent names in <tt class="literal"><span class="pre">apply</span></tt>'s initializer list must be base classes. <a class="footnote-reference" href="#plus-too" id="id7" name="id7">[2]</a> This powerful simplification is known as <strong>metafunction forwarding</strong>; we'll apply it often as the book goes on. <a class="footnote-reference" href="#edg" id="id8" name="id8">[3]</a></p> <table class="footnote" frame="void" id="plus-too" rules="none"> <colgroup><col class="label" /><col /></colgroup> <tbody valign="top"> <tr><td class="label"><a class="fn-backref" href="#id7" name="plus-too">[2]</a></td><td>In case you're wondering, the same approach could have been applied to <tt class="literal"><span class="pre">plus_f</span></tt>, but since it's a little subtle, we introduced the straightforward but verbose formulation first.</td></tr> </tbody> </table> <table class="footnote" frame="void" id="edg" rules="none"> <colgroup><col class="label" /><col /></colgroup> <tbody valign="top"> <tr><td class="label"><a class="fn-backref" href="#id8" name="edg">[3]</a></td><td>Users of EDG-based compilers should consult <a class="reference" href="./resources.html">the book's</a> Appendix C for a caveat about metafunction forwarding. You can tell whether you have an EDG compiler by checking the preprocessor symbol <tt class="literal"><span class="pre">__EDG_VERSION__</span></tt>, which is defined by all EDG-based compilers.</td></tr> </tbody> </table> <p>Syntactic tricks notwithstanding, writing trivial classes to wrap existing metafunctions is going to get boring pretty quickly. Even though the definition of <tt class="literal"><span class="pre">minus_f</span></tt> was far less verbose than that of <tt class="literal"><span class="pre">plus_f</span></tt>, it's still an awful lot to type. Fortunately, MPL gives us a <em>much</em> simpler way to pass metafunctions around. Instead of building a whole metafunction class, we can invoke <tt class="literal"><span class="pre">transform</span></tt> this way:</p> <pre class="literal-block"> typename mpl::transform<D1,D2, <strong>mpl::minus<_1,_2></strong> >::type </pre> <!-- @# Make it harmless but legit C++ so we can syntax check later example.wrap('template <class D1,class D2>', 'fff(D1,D2);') # We explain placeholders below, so we can henceforth use them # without qualification --> <p>Those funny looking arguments (<tt class="literal"><span class="pre">_1</span></tt> and <tt class="literal"><span class="pre">_2</span></tt>) are known as <strong>placeholders</strong>, and they signify that when the <tt class="literal"><span class="pre">transform</span></tt>'s <tt class="literal"><span class="pre">BinaryOperation</span></tt> is invoked, its first and second arguments will be passed on to <tt class="literal"><span class="pre">minus</span></tt> in the positions indicated by <tt class="literal"><span class="pre">_1</span></tt> and <tt class="literal"><span class="pre">_2</span></tt>, respectively. The whole type <tt class="literal"><span class="pre">mpl::minus<_1,_2></span></tt> is known as a <strong>placeholder expression</strong>.</p> <div class="note"> <p class="admonition-title first">Note</p> <p>MPL's placeholders are in the <tt class="literal"><span class="pre">mpl::placeholders</span></tt> namespace and defined in <tt class="literal"><span class="pre">boost/mpl/placeholders.hpp</span></tt>. In this book we will usually assume that you have written:</p> <pre class="literal-block"> #include<boost/mpl/placeholders.hpp> using namespace mpl::placeholders; </pre> <p>so that they can be accessed without qualification.</p> </div> <!-- @ prefix.append(str(example)) # move to common prefix ignore() --> <p>Here's our division operator written using placeholder expressions:</p> <pre class="literal-block"> template <class T, class D1, class D2> quantity< T , typename mpl::transform<D1,D2,<strong>mpl::minus<_1,_2></strong> >::type > operator/(quantity<T,D1> x, quantity<T,D2> y) { typedef typename mpl::transform<D1,D2,<strong>mpl::minus<_1,_2></strong> >::type dim; return quantity<T,dim>( x.value() / y.value() ); } </pre> <!-- @compile('all', pop = 1) --> <p>This code is considerably simpler. We can simplify it even further by factoring the code that calculates the new dimensions into its own metafunction:</p> <pre class="literal-block"> template <class D1, class D2> struct <strong>divide_dimensions</strong> : mpl::transform<D1,D2,mpl::minus<_1,_2> > // forwarding again {}; template <class T, class D1, class D2> quantity<T, typename <strong>divide_dimensions<D1,D2></strong>::type> operator/(quantity<T,D1> x, quantity<T,D2> y) { return quantity<T, typename <strong>divide_dimensions<D1,D2></strong>::type>( x.value() / y.value()); } </pre> <!-- @compile('all', pop = None) --> <p>Now we can verify our "force-on-a-laptop" computation by reversing it, as follows:</p> <pre class="literal-block"> quantity<float,mass> m2 = f/a; float rounding_error = std::abs((m2 - m).value()); </pre> <!-- @example.wrap(''' #include <cassert> #include <cmath> int main() { quantity<float,mass> m(5.0f); quantity<float,acceleration> a(9.8f); quantity<float,force> f = m * a; ''',''' assert(rounding_error < .001); }''') dimensional_analysis = stack[:-1] # save for later run('all') --> <p>If we got everything right, <tt class="literal"><span class="pre">rounding_error</span></tt> should be very close to zero. These are boring calculations, but they're just the sort of thing that could ruin a whole program (or worse) if you got them wrong. If we had written <tt class="literal"><span class="pre">a/f</span></tt> instead of <tt class="literal"><span class="pre">f/a</span></tt>, there would have been a compilation error, preventing a mistake from propagating throughout our program.</p> </div> <div class="footer-separator"></div> <table class="footer"><tr class="footer"><td class="header-group navigation-bar"><span class="navigation-group"><a href="./implementing.html" class="navigation-link">Prev</a> <a href="./higher-order.html" class="navigation-link">Next</a></span><span class="navigation-group-separator"> | </span><span class="navigation-group"><a href="./implementing.html" class="navigation-link">Back</a> Along</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>