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167 lines
10 KiB
HTML
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<!-- Copyright Aleksey Gurtovoy 2006. Distributed under the Boost -->
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<meta name="generator" content="Docutils 0.3.6: http://docutils.sourceforge.net/" />
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<title>THE BOOST MPL LIBRARY: Implementing Division</title>
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<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>
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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="./implementing-division.html" class="navigation-link">Implementing Division</a></td>
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</tr></table><div class="header-separator"></div>
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<div class="section" id="implementing-division">
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<h1><a class="toc-backref" href="./dimensional-analysis.html#id46" name="implementing-division">Implementing Division</a></h1>
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<p>Division is similar to multiplication, but instead of adding
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exponents, we must subtract them. Rather than writing out a near
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duplicate of <tt class="literal"><span class="pre">plus_f</span></tt>, we can use the following trick to make
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<tt class="literal"><span class="pre">minus_f</span></tt> much simpler:</p>
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<pre class="literal-block">
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struct minus_f
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{
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template <class T1, class T2>
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struct apply
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: mpl::minus<T1,T2> {};
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};
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</pre>
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<!-- @ # The following is OK because we showed how to get at mpl_plus
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prefix.append('#include <boost/mpl/minus.hpp>')
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compile(1) -->
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<p>Here <tt class="literal"><span class="pre">minus_f::apply</span></tt> uses inheritance to expose the nested
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<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
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write:</p>
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<pre class="literal-block">
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typedef typename ...::type type
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</pre>
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<!-- @ignore() -->
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<p>We don't have to write
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<tt class="literal"><span class="pre">typename</span></tt> here (in fact, it would be illegal), because the
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compiler knows that dependent names in <tt class="literal"><span class="pre">apply</span></tt>'s initializer
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list must be base classes. <a class="footnote-reference" href="#plus-too" id="id7" name="id7">[2]</a> This powerful
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simplification is known as <strong>metafunction forwarding</strong>; we'll apply
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it often as the book goes on. <a class="footnote-reference" href="#edg" id="id8" name="id8">[3]</a></p>
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<table class="footnote" frame="void" id="plus-too" 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="#id7" name="plus-too">[2]</a></td><td>In case you're wondering, the same approach could
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have been applied to <tt class="literal"><span class="pre">plus_f</span></tt>, but since it's a little subtle,
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we introduced the straightforward but verbose formulation
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first.</td></tr>
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</tbody>
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</table>
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<table class="footnote" frame="void" id="edg" 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="#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
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for a caveat about metafunction forwarding. You can tell whether
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you have an EDG compiler by checking the preprocessor symbol
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<tt class="literal"><span class="pre">__EDG_VERSION__</span></tt>, which is defined by all EDG-based compilers.</td></tr>
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</tbody>
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</table>
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<p>Syntactic tricks notwithstanding, writing trivial classes to wrap
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existing metafunctions is going to get boring pretty quickly. Even
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though the definition of <tt class="literal"><span class="pre">minus_f</span></tt> was far less verbose than that
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of <tt class="literal"><span class="pre">plus_f</span></tt>, it's still an awful lot to type. Fortunately, MPL gives
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us a <em>much</em> simpler way to pass metafunctions around. Instead of
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building a whole metafunction class, we can invoke <tt class="literal"><span class="pre">transform</span></tt>
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this way:</p>
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<pre class="literal-block">
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typename mpl::transform<D1,D2, <strong>mpl::minus<_1,_2></strong> >::type
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</pre>
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<!-- @# Make it harmless but legit C++ so we can syntax check later
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example.wrap('template <class D1,class D2>', 'fff(D1,D2);')
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# We explain placeholders below, so we can henceforth use them
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# without qualification -->
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<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
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<strong>placeholders</strong>, and they signify that when the <tt class="literal"><span class="pre">transform</span></tt>'s
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<tt class="literal"><span class="pre">BinaryOperation</span></tt> is invoked, its first and second arguments will
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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
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<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
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known as a <strong>placeholder expression</strong>.</p>
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<div class="note">
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<p class="admonition-title first">Note</p>
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<p>MPL's placeholders are in the <tt class="literal"><span class="pre">mpl::placeholders</span></tt>
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namespace and defined in <tt class="literal"><span class="pre">boost/mpl/placeholders.hpp</span></tt>. In
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this book we will usually assume that you have written:</p>
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<pre class="literal-block">
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#include<boost/mpl/placeholders.hpp>
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using namespace mpl::placeholders;
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</pre>
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<p>so that they can be accessed without qualification.</p>
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</div>
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<!-- @ prefix.append(str(example)) # move to common prefix
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ignore() -->
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<p>Here's our division operator written using placeholder
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expressions:</p>
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<pre class="literal-block">
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template <class T, class D1, class D2>
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quantity<
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T
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, typename mpl::transform<D1,D2,<strong>mpl::minus<_1,_2></strong> >::type
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>
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operator/(quantity<T,D1> x, quantity<T,D2> y)
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{
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typedef typename
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mpl::transform<D1,D2,<strong>mpl::minus<_1,_2></strong> >::type dim;
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return quantity<T,dim>( x.value() / y.value() );
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}
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</pre>
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<!-- @compile('all', pop = 1) -->
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<p>This code is considerably simpler. We can simplify it even further
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by factoring the code that calculates the new dimensions into its
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own metafunction:</p>
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<pre class="literal-block">
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template <class D1, class D2>
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struct <strong>divide_dimensions</strong>
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: mpl::transform<D1,D2,mpl::minus<_1,_2> > // forwarding again
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{};
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template <class T, class D1, class D2>
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quantity<T, typename <strong>divide_dimensions<D1,D2></strong>::type>
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operator/(quantity<T,D1> x, quantity<T,D2> y)
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{
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return quantity<T, typename <strong>divide_dimensions<D1,D2></strong>::type>(
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x.value() / y.value());
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}
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</pre>
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<!-- @compile('all', pop = None) -->
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<p>Now we can verify our "force-on-a-laptop" computation by reversing
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it, as follows:</p>
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<pre class="literal-block">
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quantity<float,mass> m2 = f/a;
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float rounding_error = std::abs((m2 - m).value());
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</pre>
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<!-- @example.wrap('''
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#include <cassert>
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#include <cmath>
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int main()
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{
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quantity<float,mass> m(5.0f);
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quantity<float,acceleration> a(9.8f);
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quantity<float,force> f = m * a;
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''','''
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assert(rounding_error < .001);
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}''')
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dimensional_analysis = stack[:-1] # save for later
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run('all') -->
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<p>If we got everything right, <tt class="literal"><span class="pre">rounding_error</span></tt> should be very close
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to zero. These are boring calculations, but they're just the sort
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of thing that could ruin a whole program (or worse) if you got them
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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
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been a compilation error, preventing a mistake from propagating
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throughout our program.</p>
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</div>
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