1<?xml version="1.0" encoding="utf-8" ?> 2<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> 3<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"> 4<!-- Copyright Aleksey Gurtovoy 2006. Distributed under the Boost --> 5<!-- Software License, Version 1.0. (See accompanying --> 6<!-- file LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt) --> 7<head> 8<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> 9<meta name="generator" content="Docutils 0.3.6: http://docutils.sourceforge.net/" /> 10<title>THE BOOST MPL LIBRARY: Implementing Division</title> 11<link rel="stylesheet" href="../style.css" type="text/css" /> 12</head> 13<body class="docframe"> 14<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> 15<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> 16</tr></table><div class="header-separator"></div> 17<div class="section" id="implementing-division"> 18<h1><a class="toc-backref" href="./dimensional-analysis.html#id46" name="implementing-division">Implementing Division</a></h1> 19<p>Division is similar to multiplication, but instead of adding 20exponents, we must subtract them. Rather than writing out a near 21duplicate of <tt class="literal"><span class="pre">plus_f</span></tt>, we can use the following trick to make 22<tt class="literal"><span class="pre">minus_f</span></tt> much simpler:</p> 23<pre class="literal-block"> 24struct minus_f 25{ 26 template <class T1, class T2> 27 struct apply 28 : mpl::minus<T1,T2> {}; 29}; 30</pre> 31<!-- @ # The following is OK because we showed how to get at mpl_plus 32prefix.append('#include <boost/mpl/minus.hpp>') 33compile(1) --> 34<p>Here <tt class="literal"><span class="pre">minus_f::apply</span></tt> uses inheritance to expose the nested 35<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 36write:</p> 37<pre class="literal-block"> 38typedef typename ...::type type 39</pre> 40<!-- @ignore() --> 41<p>We don't have to write 42<tt class="literal"><span class="pre">typename</span></tt> here (in fact, it would be illegal), because the 43compiler knows that dependent names in <tt class="literal"><span class="pre">apply</span></tt>'s initializer 44list must be base classes. <a class="footnote-reference" href="#plus-too" id="id7" name="id7">[2]</a> This powerful 45simplification is known as <strong>metafunction forwarding</strong>; we'll apply 46it often as the book goes on. <a class="footnote-reference" href="#edg" id="id8" name="id8">[3]</a></p> 47<table class="footnote" frame="void" id="plus-too" rules="none"> 48<colgroup><col class="label" /><col /></colgroup> 49<tbody valign="top"> 50<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 51have been applied to <tt class="literal"><span class="pre">plus_f</span></tt>, but since it's a little subtle, 52we introduced the straightforward but verbose formulation 53first.</td></tr> 54</tbody> 55</table> 56<table class="footnote" frame="void" id="edg" rules="none"> 57<colgroup><col class="label" /><col /></colgroup> 58<tbody valign="top"> 59<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 60for a caveat about metafunction forwarding. You can tell whether 61you have an EDG compiler by checking the preprocessor symbol 62<tt class="literal"><span class="pre">__EDG_VERSION__</span></tt>, which is defined by all EDG-based compilers.</td></tr> 63</tbody> 64</table> 65<p>Syntactic tricks notwithstanding, writing trivial classes to wrap 66existing metafunctions is going to get boring pretty quickly. Even 67though the definition of <tt class="literal"><span class="pre">minus_f</span></tt> was far less verbose than that 68of <tt class="literal"><span class="pre">plus_f</span></tt>, it's still an awful lot to type. Fortunately, MPL gives 69us a <em>much</em> simpler way to pass metafunctions around. Instead of 70building a whole metafunction class, we can invoke <tt class="literal"><span class="pre">transform</span></tt> 71this way:</p> 72<pre class="literal-block"> 73typename mpl::transform<D1,D2, <strong>mpl::minus<_1,_2></strong> >::type 74</pre> 75<!-- @# Make it harmless but legit C++ so we can syntax check later 76example.wrap('template <class D1,class D2>', 'fff(D1,D2);') 77 78# We explain placeholders below, so we can henceforth use them 79# without qualification --> 80<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 81<strong>placeholders</strong>, and they signify that when the <tt class="literal"><span class="pre">transform</span></tt>'s 82<tt class="literal"><span class="pre">BinaryOperation</span></tt> is invoked, its first and second arguments will 83be 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 84<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 85known as a <strong>placeholder expression</strong>.</p> 86<div class="note"> 87<p class="admonition-title first">Note</p> 88<p>MPL's placeholders are in the <tt class="literal"><span class="pre">mpl::placeholders</span></tt> 89namespace and defined in <tt class="literal"><span class="pre">boost/mpl/placeholders.hpp</span></tt>. In 90this book we will usually assume that you have written:</p> 91<pre class="literal-block"> 92#include<boost/mpl/placeholders.hpp> 93using namespace mpl::placeholders; 94</pre> 95<p>so that they can be accessed without qualification.</p> 96</div> 97<!-- @ prefix.append(str(example)) # move to common prefix 98ignore() --> 99<p>Here's our division operator written using placeholder 100expressions:</p> 101<pre class="literal-block"> 102template <class T, class D1, class D2> 103quantity< 104 T 105 , typename mpl::transform<D1,D2,<strong>mpl::minus<_1,_2></strong> >::type 106> 107operator/(quantity<T,D1> x, quantity<T,D2> y) 108{ 109 typedef typename 110 mpl::transform<D1,D2,<strong>mpl::minus<_1,_2></strong> >::type dim; 111 112 return quantity<T,dim>( x.value() / y.value() ); 113} 114</pre> 115<!-- @compile('all', pop = 1) --> 116<p>This code is considerably simpler. We can simplify it even further 117by factoring the code that calculates the new dimensions into its 118own metafunction:</p> 119<pre class="literal-block"> 120template <class D1, class D2> 121struct <strong>divide_dimensions</strong> 122 : mpl::transform<D1,D2,mpl::minus<_1,_2> > // forwarding again 123{}; 124 125template <class T, class D1, class D2> 126quantity<T, typename <strong>divide_dimensions<D1,D2></strong>::type> 127operator/(quantity<T,D1> x, quantity<T,D2> y) 128{ 129 return quantity<T, typename <strong>divide_dimensions<D1,D2></strong>::type>( 130 x.value() / y.value()); 131} 132</pre> 133<!-- @compile('all', pop = None) --> 134<p>Now we can verify our "force-on-a-laptop" computation by reversing 135it, as follows:</p> 136<pre class="literal-block"> 137quantity<float,mass> m2 = f/a; 138float rounding_error = std::abs((m2 - m).value()); 139</pre> 140<!-- @example.wrap(''' 141#include <cassert> 142#include <cmath> 143int main() 144{ 145 quantity<float,mass> m(5.0f); 146 quantity<float,acceleration> a(9.8f); 147 quantity<float,force> f = m * a; 148''',''' 149 assert(rounding_error < .001); 150}''') 151 152dimensional_analysis = stack[:-1] # save for later 153 154run('all') --> 155<p>If we got everything right, <tt class="literal"><span class="pre">rounding_error</span></tt> should be very close 156to zero. These are boring calculations, but they're just the sort 157of thing that could ruin a whole program (or worse) if you got them 158wrong. 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 159been a compilation error, preventing a mistake from propagating 160throughout our program.</p> 161</div> 162 163<div class="footer-separator"></div> 164<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> 165</tr></table></body> 166</html> 167