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- <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>
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