| <?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> |
