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- <body class="article toc2 toc-left">
- <div id="header">
- <h1>Simple C++11 metaprogramming</h1>
- <div class="details">
- <span id="author" class="author">Peter Dimov</span><br>
- <span id="revdate">2015-05-26</span>
- </div>
- <div id="toc" class="toc2">
- <div id="toctitle">Table of Contents</div>
- <ul class="sectlevel1">
- <li><a href="#c11_changes_the_playing_field">C++11 changes the playing field</a></li>
- <li><a href="#type_lists_and_mp_rename">Type lists and mp_rename</a></li>
- <li><a href="#mp_transform">mp_transform</a></li>
- <li><a href="#mp_transform_part_two">mp_transform, part two</a></li>
- <li><a href="#the_infamous_tuple_cat_challenge">The infamous tuple_cat challenge</a></li>
- <li><a href="#higher_order_metaprogramming_or_lack_thereof">Higher order metaprogramming, or lack thereof</a></li>
- <li><a href="#one_more_thing">One more thing</a></li>
- <li><a href="#conclusion">Conclusion</a></li>
- <li><a href="#further_reading">Further reading</a></li>
- </ul>
- </div>
- </div>
- <div id="content">
- <div id="preamble">
- <div class="sectionbody">
- <div class="paragraph lead">
- <p><em>With variadic templates, parameter packs and template aliases</em></p>
- </div>
- <div class="admonitionblock note">
- <table>
- <tr>
- <td class="icon">
- <div class="title">Note</div>
- </td>
- <td class="content">
- I was motivated to write this after I read Eric Niebler’s
- thought-provoking
- <a href="http://ericniebler.com/2014/11/13/tiny-metaprogramming-library/">Tiny
- Metaprogramming Library</a> article. Thanks Eric.
- </td>
- </tr>
- </table>
- </div>
- </div>
- </div>
- <div class="sect1">
- <h2 id="c11_changes_the_playing_field">C++11 changes the playing field</h2>
- <div class="sectionbody">
- <div class="paragraph">
- <p>The wide acceptance of <a href="http://www.boost.org/libs/mpl">Boost.MPL</a> made C++
- metaprogramming seem a solved problem. Perhaps MPL wasn’t ideal, but it was
- good enough to the point that there wasn’t really a need to seek or produce
- alternatives.</p>
- </div>
- <div class="paragraph">
- <p>C++11 changed the playing field. The addition of variadic templates with
- their associated parameter packs added a compile-time list of types structure
- directly into the language. Whereas before every metaprogramming library
- defined its own type list, and MPL defined several, in C++11, type lists are
- as easy as</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>// C++11
- template<class... T> struct type_list {};</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and there is hardly a reason to use anything else.</p>
- </div>
- <div class="paragraph">
- <p>Template aliases are another game changer. Previously, "metafunctions", that
- is, templates that took one type and produced another, looked like</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>// C++03
- template<class T> struct add_pointer { typedef T* type; };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and were used in the following manner:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>// C++03
- typedef typename add_pointer<X>::type Xp;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>In C++11, metafunctions can be template aliases, instead of class templates:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>// C++11
- template<class T> using add_pointer = T*;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>The above example use then becomes</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>// C++11
- typedef add_pointer<X> Xp;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>or, if you prefer to be seen as C++11-savvy,</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>// C++11
- using Xp = add_pointer<X>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>This is a considerable improvement in more complex expressions:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>// C++03
- typedef
- typename add_reference<
- typename add_const<
- typename add_pointer<X>::type
- >::type
- >::type Xpcr;</code></pre>
- </div>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>// C++11
- using Xpcr = add_reference<add_const<add_pointer<X>>>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>(The example also takes advantage of another C++11 feature - you can now use
- <code>>></code> to close templates without it being interpreted as a right shift.)</p>
- </div>
- <div class="paragraph">
- <p>In addition, template aliases can be passed to template template parameters:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>// C++11
- template<template<class... T> class F> struct X
- {
- };
- X<add_pointer>; // works!</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>These language improvements allow for C++11 metaprogramming that is
- substantially different than its idiomatic C++03 equivalent. Boost.MPL is no
- longer good enough, and <em>something must be done</em>. But what?</p>
- </div>
- </div>
- </div>
- <div class="sect1">
- <h2 id="type_lists_and_mp_rename">Type lists and mp_rename</h2>
- <div class="sectionbody">
- <div class="paragraph">
- <p>Let’s start with the basics. Our basic data structure will be the type list:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... T> struct mp_list {};</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Why the <code>mp_</code> prefix? mp obviously stands for metaprogramming, but could we not
- have used a namespace?</p>
- </div>
- <div class="paragraph">
- <p>Indeed we could have. Past experience with Boost.MPL however indicates that
- name conflicts between our metaprogramming primitives and standard identifiers
- (such as <code>list</code>) and keywords (such as <code>if</code>, <code>int</code> or <code>true</code>) will be common
- and will be a source of problems. With a prefix, we avoid all that trouble.</p>
- </div>
- <div class="paragraph">
- <p>So we have our type list and can put things into it:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>using list = mp_list<int, char, float, double, void>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>but can’t do anything else with it yet. We’ll need a library of primitives that
- operate on <code>mp_list</code>s. But before we get into that, let’s consider another
- interesting question first.</p>
- </div>
- <div class="paragraph">
- <p>Suppose we have our library of primitives that can do things with a <code>mp_list</code>,
- but some other code hands us a type list that is not an <code>mp_list</code>, such as for
- example an <code>std::tuple<int, float, void*></code>, or
- <code><a href="http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2014/n4115.html">std::packer</a><int,
- float, void*></code>.</p>
- </div>
- <div class="paragraph">
- <p>Suppose we need to modify this external list of types in some manner (change
- the types into pointers, perhaps) and give back the transformed result in the
- form it was given to us, <code>std::tuple<int*, float*, void**></code> in the first
- case and <code>std::packer<int*, float*, void**></code> in the second.</p>
- </div>
- <div class="paragraph">
- <p>To do that, we need to first convert <code>std::tuple<int, float, void*></code> to
- <code>mp_list<int, float, void*></code>, apply <code>add_pointer</code> to each element obtaining
- <code>mp_list<int*, float*, void**></code>, then convert that back to <code>std::tuple</code>.</p>
- </div>
- <div class="paragraph">
- <p>These conversion steps are a quite common occurrence, and we’ll write a
- primitive that helps us perform them, called <code>mp_rename</code>. We want</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>mp_rename<std::tuple<int, float, void*>, mp_list></code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>to give us</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>mp_list<int, float, void*></code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and conversely,</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>mp_rename<mp_list<int, float, void*>, std::tuple></code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>to give us</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>std::tuple<int, float, void*></code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Here is the implementation of <code>mp_rename</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class A, template<class...> class B> struct mp_rename_impl;
- template<template<class...> class A, class... T, template<class...> class B>
- struct mp_rename_impl<A<T...>, B>
- {
- using type = B<T...>;
- };
- template<class A, template<class...> class B>
- using mp_rename = typename mp_rename_impl<A, B>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>(This pattern of a template alias forwarding to a class template doing the
- actual work is common; class templates can be specialized, whereas template
- aliases cannot.)</p>
- </div>
- <div class="paragraph">
- <p>Note that <code>mp_rename</code> does not treat any list type as special, not even
- <code>mp_list</code>; it can rename any variadic class template into any other. You could
- use it to rename <code>std::packer</code> to <code>std::tuple</code> to <code>std::variant</code> (once there is
- such a thing) and it will happily oblige.</p>
- </div>
- <div class="paragraph">
- <p>In fact, it can even rename non-variadic class templates, as in the following
- examples:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>mp_rename<std::pair<int, float>, std::tuple> // -> std::tuple<int, float>
- mp_rename<mp_list<int, float>, std::pair> // -> std::pair<int, float>
- mp_rename<std::shared_ptr<int>, std::unique_ptr> // -> std::unique_ptr<int></code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>There is a limit to the magic; <code>unique_ptr</code> can’t be renamed to <code>shared_ptr</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>mp_rename<std::unique_ptr<int>, std::shared_ptr> // error</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>because <code>unique_ptr<int></code> is actually <code>unique_ptr<int,
- std::default_delete<int>></code> and <code>mp_rename</code> renames it to <code>shared_ptr<int,
- std::default_delete<int>></code>, which doesn’t compile. But it still works in many
- more cases than one would naively expect at first.</p>
- </div>
- <div class="paragraph">
- <p>With conversions no longer a problem, let’s move on to primitives and define a
- simple one, <code>mp_size</code>, for practice. We want <code>mp_size<mp_list<T...>></code> to
- give us the number of elements in the list, that is, the value of the
- expression <code>sizeof...(T)</code>.</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class L> struct mp_size_impl;
- template<class... T> struct mp_size_impl<mp_list<T...>>
- {
- using type = std::integral_constant<std::size_t, sizeof...(T)>;
- };
- template<class L> using mp_size = typename mp_size_impl<L>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>This is relatively straightforward, except for the <code>std::integral_constant</code>.
- What is it and why do we need it?</p>
- </div>
- <div class="paragraph">
- <p><code>std::integral_constant</code> is a standard C++11 type that wraps an integral
- constant (that is, a compile-time constant integer value) into a type.</p>
- </div>
- <div class="paragraph">
- <p>Since metaprogramming operates on type lists, which can only hold types, it’s
- convenient to represent compile-time constants as types. This allows us to
- treat lists of types and lists of values in a uniform manner. It is therefore
- idiomatic in metaprogramming to take and return types instead of values, and
- this is what we have done. If at some later point we want the actual value, we
- can use the expression <code>mp_size<L>::value</code> to retrieve it.</p>
- </div>
- <div class="paragraph">
- <p>We now have our <code>mp_size</code>, but you may have noticed that there’s an interesting
- difference between <code>mp_size</code> and <code>mp_rename</code>. Whereas I made a point of
- <code>mp_rename</code> not treating <code>mp_list</code> as a special case, <code>mp_size</code> very much does:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... T> struct mp_size_impl<mp_list<T...>></code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Is this really necessary? Can we not use the same technique in the
- implementation of <code>mp_size</code> as we did in <code>mp_rename</code>?</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class L> struct mp_size_impl;
- template<template<class...> class L, class... T> struct mp_size_impl<L<T...>>
- {
- using type = std::integral_constant<std::size_t, sizeof...(T)>;
- };
- template<class L> using mp_size = typename mp_size_impl<L>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Yes, we very much can, and this improvement allows us to use <code>mp_size</code> on any
- other type lists, such as <code>std::tuple</code>. It turns <code>mp_size</code> into a truly generic
- primitive.</p>
- </div>
- <div class="paragraph">
- <p>This is nice. It is so nice that I’d argue that all our metaprogramming
- primitives ought to have this property. If someone hands us a type list in the
- form of an <code>std::tuple</code>, we should be able to operate on it directly, avoiding
- the conversions to and from <code>mp_list</code>.</p>
- </div>
- <div class="paragraph">
- <p>So do we no longer have any need for <code>mp_rename</code>? Not quite. Apart from the
- fact that sometimes we really do need to rename type lists, there is another
- surprising task for which <code>mp_rename</code> is useful.</p>
- </div>
- <div class="paragraph">
- <p>To illustrate it, let me introduce the primitive <code>mp_length</code>. It’s similar to
- <code>mp_size</code>, but while <code>mp_size</code> takes a type list as an argument, <code>mp_length</code>
- takes a variadic parameter pack and returns its length; or, stated differently,
- it returns its number of arguments:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... T> using mp_length =
- std::integral_constant<std::size_t, sizeof...(T)>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>How would we implement <code>mp_size</code> in terms of <code>mp_length</code>? One option is to just
- substitute the implementation of the latter into the former:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<template<class...> class L, class... T> struct mp_size_impl<L<T...>>
- {
- using type = mp_length<T...>;
- };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>but there is another way, much less mundane. Think about what <code>mp_size</code> does.
- It takes the argument</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code><strong>mp_list</strong><int, void, float></code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and returns</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code><strong>mp_length</strong><int, void, float></code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Do we already have a primitive that does a similar thing?</p>
- </div>
- <div class="paragraph">
- <p>(Not much of a choice, is there?)</p>
- </div>
- <div class="paragraph">
- <p>Indeed we have, and it’s called <code>mp_rename</code>.</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class L> using mp_size = mp_rename<L, mp_length>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>I don’t know about you, but I find this technique fascinating. It exploits the
- structural similarity between a list, <code>L<T...></code>, and a metafunction "call",
- <code>F<T...></code>, and the fact that the language sees the things the same way and
- allows us to pass the template alias <code>mp_length</code> to <code>mp_rename</code> as if it were
- an ordinary class template such as <code>mp_list</code>.</p>
- </div>
- <div class="paragraph">
- <p>(Other metaprogramming libraries provide a dedicated <code>apply</code> primitive for
- this job. <code>apply<F, L></code> calls the metafunction <code>F</code> with the contents of the
- list <code>L</code>. We’ll add an alias <code>mp_apply<F, L></code> that calls <code>mp_rename<L, F></code> for
- readability.)</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<template<class...> class F, class L> using mp_apply = mp_rename<L, F>;</code></pre>
- </div>
- </div>
- </div>
- </div>
- <div class="sect1">
- <h2 id="mp_transform">mp_transform</h2>
- <div class="sectionbody">
- <div class="paragraph">
- <p>Let’s revisit the example I gave earlier - someone hands us <code>std::tuple<X, Y,
- Z></code> and we need to compute <code>std::tuple<X*, Y*, Z*></code>. We already have
- <code>add_pointer</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class T> using add_pointer = T*;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>so we just need to apply it to each element of the input tuple.</p>
- </div>
- <div class="paragraph">
- <p>The algorithm that takes a function and a list and applies the function to each
- element is called <code>transform</code> in Boost.MPL and the STL and <code>map</code> in functional
- languages. We’ll use <code>transform</code>, for consistency with the established C++
- practice (<code>map</code> is a data structure in both the STL and Boost.MPL.)</p>
- </div>
- <div class="paragraph">
- <p>We’ll call our algorithm <code>mp_transform</code>, and <code>mp_transform<F, L></code> will apply
- <code>F</code> to each element of <code>L</code> and return the result. Usually, the argument order
- is reversed and the function comes last. Our reasons to put it at the front
- will become evident later.</p>
- </div>
- <div class="paragraph">
- <p>There are many ways to implement <code>mp_transform</code>; the one we’ll pick will make
- use of another primitive, <code>mp_push_front</code>. <code>mp_push_front<L, T></code>, as its name
- implies, adds <code>T</code> as a first element in <code>L</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class L, class T> struct mp_push_front_impl;
- template<template<class...> class L, class... U, class T>
- struct mp_push_front_impl<L<U...>, T>
- {
- using type = L<T, U...>;
- };
- template<class L, class T>
- using mp_push_front = typename mp_push_front_impl<L, T>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>There is no reason to constrain <code>mp_push_front</code> to a single element though. In
- C++11, variadic templates should be our default choice, and the
- implementation of <code>mp_push_front</code> that can take an arbitrary number of elements
- is almost identical:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class L, class... T> struct mp_push_front_impl;
- template<template<class...> class L, class... U, class... T>
- struct mp_push_front_impl<L<U...>, T...>
- {
- using type = L<T..., U...>;
- };
- template<class L, class... T>
- using mp_push_front = typename mp_push_front_impl<L, T...>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>On to <code>mp_transform</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<template<class...> class F, class L> struct mp_transform_impl;
- template<template<class...> class F, class L>
- using mp_transform = typename mp_transform_impl<F, L>::type;
- template<template<class...> class F, template<class...> class L>
- struct mp_transform_impl<F, L<>>
- {
- using type = L<>;
- };
- template<template<class...> class F, template<class...> class L, class T1, class... T>
- struct mp_transform_impl<F, L<T1, T...>>
- {
- using _first = F<T1>;
- using _rest = mp_transform<F, L<T...>>;
- using type = mp_push_front<_rest, _first>;
- };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>This is a straightforward recursive implementation that should be familiar to
- people with functional programming background.</p>
- </div>
- <div class="paragraph">
- <p>Can we do better? It turns out that in C++11, we can.</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<template<class...> class F, class L> struct mp_transform_impl;
- template<template<class...> class F, class L>
- using mp_transform = typename mp_transform_impl<F, L>::type;
- template<template<class...> class F, template<class...> class L, class... T>
- struct mp_transform_impl<F, L<T...>>
- {
- using type = L<F<T>...>;
- };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Here we take advantage of the fact that pack expansion is built into the
- language, so the <code>F<T>...</code> part does all the iteration work for us.</p>
- </div>
- <div class="paragraph">
- <p>We can now solve our original challenge: given an <code>std::tuple</code> of types, return
- an <code>std::tuple</code> of pointers to these types:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>using input = std::tuple<int, void, float>;
- using expected = std::tuple<int*, void*, float*>;
- using result = mp_transform<add_pointer, input>;
- static_assert( std::is_same<result, expected>::value, "" );</code></pre>
- </div>
- </div>
- </div>
- </div>
- <div class="sect1">
- <h2 id="mp_transform_part_two">mp_transform, part two</h2>
- <div class="sectionbody">
- <div class="paragraph">
- <p>What if we had a pair of tuples as input, and had to produce the corresponding
- tuple of pairs? For example, given</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>using input = std::pair<std::tuple<X1, X2, X3>, std::tuple<Y1, Y2, Y3>>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>we had to produce</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>using expected = std::tuple<std::pair<X1, Y1>, std::pair<X2, Y2>, std::pair<X3, Y3>>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>We need to take the two lists, represented by tuples in the input, and combine
- them pairwise by using <code>std::pair</code>. If we think of <code>std::pair</code> as a function
- <code>F</code>, this task appears very similar to <code>mp_transform</code>, except we need to use a
- binary function and two lists.</p>
- </div>
- <div class="paragraph">
- <p>Changing our unary transform algorithm into a binary one isn’t hard:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<template<class...> class F, class L1, class L2>
- struct mp_transform2_impl;
- template<template<class...> class F, class L1, class L2>
- using mp_transform2 = typename mp_transform2_impl<F, L1, L2>::type;
- template<template<class...> class F,
- template<class...> class L1, class... T1,
- template<class...> class L2, class... T2>
- struct mp_transform2_impl<F, L1<T1...>, L2<T2...>>
- {
- static_assert( sizeof...(T1) == sizeof...(T2),
- "The arguments of mp_transform2 should be of the same size" );
- using type = L1<F<T1,T2>...>;
- };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and we can now do</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>using input = std::pair<std::tuple<X1, X2, X3>, std::tuple<Y1, Y2, Y3>>;
- using expected = std::tuple<std::pair<X1, Y1>, std::pair<X2, Y2>, std::pair<X3, Y3>>;
- using result = mp_transform2<std::pair, input::first_type, input::second_type>;
- static_assert( std::is_same<result, expected>::value, "" );</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>again exploiting the similarity between metafunctions and ordinary class
- templates such as <code>std::pair</code>, this time in the other direction; we pass
- <code>std::pair</code> where <code>mp_transform2</code> expects a metafunction.</p>
- </div>
- <div class="paragraph">
- <p>Do we <em>have</em> to use separate transform algorithms for each arity though? If we
- need a transform algorithm that takes a ternary function and three lists,
- should we name it <code>mp_transform3</code>? No, this is exactly why we put the function
- first. We just have to change <code>mp_transform</code> to be variadic:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<template<class...> class F, class... L> struct mp_transform_impl;
- template<template<class...> class F, class... L>
- using mp_transform = typename mp_transform_impl<F, L...>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and then add the unary and binary specializations:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<template<class...> class F, template<class...> class L, class... T>
- struct mp_transform_impl<F, L<T...>>
- {
- using type = L<F<T>...>;
- };
- template<template<class...> class F,
- template<class...> class L1, class... T1,
- template<class...> class L2, class... T2>
- struct mp_transform_impl<F, L1<T1...>, L2<T2...>>
- {
- static_assert( sizeof...(T1) == sizeof...(T2),
- "The arguments of mp_transform should be of the same size" );
- using type = L1<F<T1,T2>...>;
- };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>We can also add ternary and further specializations.</p>
- </div>
- <div class="paragraph">
- <p>Is it possible to implement the truly variadic <code>mp_transform</code>, one that works
- with an arbitrary number of lists? It is in principle, and I’ll show one
- possible abridged implementation here for completeness:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<template<class...> class F, class E, class... L>
- struct mp_transform_impl;
- template<template<class...> class F, class... L>
- using mp_transform = typename mp_transform_impl<F, mp_empty<L...>, L...>::type;
- template<template<class...> class F, class L1, class... L>
- struct mp_transform_impl<F, mp_true, L1, L...>
- {
- using type = mp_clear<L1>;
- };
- template<template<class...> class F, class... L>
- struct mp_transform_impl<F, mp_false, L...>
- {
- using _first = F< typename mp_front_impl<L>::type... >;
- using _rest = mp_transform< F, typename mp_pop_front_impl<L>::type... >;
- using type = mp_push_front<_rest, _first>;
- };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>but will omit the primitives that it uses. These are</p>
- </div>
- <div class="ulist">
- <ul>
- <li>
- <p><code>mp_true</code> — an alias for <code>std::integral_constant<bool, true></code>.</p>
- </li>
- <li>
- <p><code>mp_false</code> — an alias for <code>std::integral_constant<bool, false></code>.</p>
- </li>
- <li>
- <p><code>mp_empty<L...></code> — returns <code>mp_true</code> if all lists are empty, <code>mp_false</code>
- otherwise.</p>
- </li>
- <li>
- <p><code>mp_clear<L></code> — returns an empty list of the same type as <code>L</code>.</p>
- </li>
- <li>
- <p><code>mp_front<L></code> — returns the first element of <code>L</code>.</p>
- </li>
- <li>
- <p><code>mp_pop_front<L></code> — returns <code>L</code> without its first element.</p>
- </li>
- </ul>
- </div>
- <div class="paragraph">
- <p>There is one interesting difference between the recursive <code>mp_transform</code>
- implementation and the language-based one. <code>mp_transform<add_pointer,
- std::pair<int, float>></code> works with the <code>F<T>...</code> implementation and fails
- with the recursive one, because <code>std::pair</code> is not a real type list and can
- only hold exactly two types.</p>
- </div>
- </div>
- </div>
- <div class="sect1">
- <h2 id="the_infamous_tuple_cat_challenge">The infamous tuple_cat challenge</h2>
- <div class="sectionbody">
- <div class="paragraph">
- <p>Eric Niebler, in his
- <a href="http://ericniebler.com/2014/11/13/tiny-metaprogramming-library/">Tiny
- Metaprogramming Library</a> article, gives the function
- <a href="http://en.cppreference.com/w/cpp/utility/tuple/tuple_cat"><code>std::tuple_cat</code></a> as a
- kind of a metaprogramming challenge. <code>tuple_cat</code> is a variadic template
- function that takes a number of tuples and concatenates them into another
- <code>std::tuple</code>. This is Eric’s solution:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>namespace detail
- {
- template<typename Ret, typename...Is, typename ...Ks,
- typename Tuples>
- Ret tuple_cat_(typelist<Is...>, typelist<Ks...>,
- Tuples tpls)
- {
- return Ret{std::get<Ks::value>(
- std::get<Is::value>(tpls))...};
- }
- }
- template<typename...Tuples,
- typename Res =
- typelist_apply_t<
- meta_quote<std::tuple>,
- typelist_cat_t<typelist<as_typelist_t<Tuples>...> > > >
- Res tuple_cat(Tuples &&... tpls)
- {
- static constexpr std::size_t N = sizeof...(Tuples);
- // E.g. [0,0,0,2,2,2,3,3]
- using inner =
- typelist_cat_t<
- typelist_transform_t<
- typelist<as_typelist_t<Tuples>...>,
- typelist_transform_t<
- as_typelist_t<make_index_sequence<N> >,
- meta_quote<meta_always> >,
- meta_quote<typelist_transform_t> > >;
- // E.g. [0,1,2,0,1,2,0,1]
- using outer =
- typelist_cat_t<
- typelist_transform_t<
- typelist<as_typelist_t<Tuples>...>,
- meta_compose<
- meta_quote<as_typelist_t>,
- meta_quote_i<std::size_t, make_index_sequence>,
- meta_quote<typelist_size_t> > > >;
- return detail::tuple_cat_<Res>(
- inner{},
- outer{},
- std::forward_as_tuple(std::forward<Tuples>(tpls)...));
- }</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>All right, challenge accepted. Let’s see what we can do.</p>
- </div>
- <div class="paragraph">
- <p>As Eric explains, this implementation relies on the clever trick of packing the
- input tuples into a tuple, creating two arrays of indices, <code>inner</code> and <code>outer</code>,
- then indexing the outer tuple with the outer indices and the result, which is
- one of our input tuples, with the inner indices.</p>
- </div>
- <div class="paragraph">
- <p>So, for example, if tuple_cat is invoked as</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>std::tuple<int, short, long> t1;
- std::tuple<> t2;
- std::tuple<float, double, long double> t3;
- std::tuple<void*, char*> t4;
- auto res = tuple_cat(t1, t2, t3, t4);</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>we’ll create the tuple</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>std::tuple<std::tuple<int, short, long>, std::tuple<>,
- std::tuple<float, double, long double>, std::tuple<void*, char*>> t{t1, t2, t3, t4};</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and then extract the elements of t via</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>std::get<0>(std::get<0>(t)), // t1[0]
- std::get<1>(std::get<0>(t)), // t1[1]
- std::get<2>(std::get<0>(t)), // t1[2]
- std::get<0>(std::get<2>(t)), // t3[0]
- std::get<1>(std::get<2>(t)), // t3[1]
- std::get<2>(std::get<2>(t)), // t3[2]
- std::get<0>(std::get<3>(t)), // t4[0]
- std::get<1>(std::get<3>(t)), // t4[1]</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>(<code>t2</code> is empty, so we take nothing from it.)</p>
- </div>
- <div class="paragraph">
- <p>The first column of integers is the <code>outer</code> array, the second one - the <code>inner</code>
- array, and these are what we need to compute. But first, let’s deal with the
- return type of <code>tuple_cat</code>.</p>
- </div>
- <div class="paragraph">
- <p>The return type of <code>tuple_cat</code> is just the concatenation of the arguments,
- viewed as type lists. The metaprogramming algorithm that concatenates lists is
- called
- <a href="https://ericniebler.github.io/meta/group__transformation.html"><code>meta::concat</code></a>
- in Eric Niebler’s <a href="https://github.com/ericniebler/meta">Meta</a> library, but I’ll
- call it <code>mp_append</code>, after its classic Lisp name.</p>
- </div>
- <div class="paragraph">
- <p>(Lisp is today’s equivalent of Latin. Educated people are supposed to have
- studied and forgotten it.)</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... L> struct mp_append_impl;
- template<class... L> using mp_append = typename mp_append_impl<L...>::type;
- template<> struct mp_append_impl<>
- {
- using type = mp_list<>;
- };
- template<template<class...> class L, class... T> struct mp_append_impl<L<T...>>
- {
- using type = L<T...>;
- };
- template<template<class...> class L1, class... T1,
- template<class...> class L2, class... T2, class... Lr>
- struct mp_append_impl<L1<T1...>, L2<T2...>, Lr...>
- {
- using type = mp_append<L1<T1..., T2...>, Lr...>;
- };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>That was fairly easy. There are other ways to implement <code>mp_append</code>, but this
- one demonstrates how the language does most of the work for us via pack
- expansion. This is a common theme in C++11.</p>
- </div>
- <div class="paragraph">
- <p>Note how <code>mp_append</code> returns the same list type as its first argument. Of
- course, in the case in which no arguments are given, there is no first argument
- from which to take the type, so I’ve arbitrarily chosen to return an empty
- <code>mp_list</code>.</p>
- </div>
- <div class="paragraph">
- <p>We’re now ready with the declaration of <code>tuple_cat</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... Tp,
- class R = mp_append<typename std::remove_reference<Tp>::type...>>
- R tuple_cat( Tp &&... tp );</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>The reason we need <code>remove_reference</code> is because of the rvalue reference
- parameters, used to implement perfect forwarding. If the argument is an lvalue,
- such as for example <code>t1</code> above, its corresponding type will be a reference to a
- tuple — <code>std::tuple<int, short, long>&</code> in <code>t1</code>'s case. Our primitives do
- not recognize references to tuples as type lists, so we need to strip them off.</p>
- </div>
- <div class="paragraph">
- <p>There are two problems with our return type computation though. One, what if
- <code>tuple_cat</code> is called without any arguments? We return <code>mp_list<></code> in that
- case, but the correct result is <code>std::tuple<></code>.</p>
- </div>
- <div class="paragraph">
- <p>Two, what if we call <code>tuple_cat</code> with a first argument that is a <code>std::pair</code>?
- We’ll try to append more elements to <code>std::pair</code>, and it will fail.</p>
- </div>
- <div class="paragraph">
- <p>We can solve both our problems by using an empty tuple as the first argument to
- <code>mp_append</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... Tp,
- class R = mp_append<std::tuple<>, typename std::remove_reference<Tp>::type...>>
- R tuple_cat( Tp &&... tp );</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>With the return type taken care of, let’s now move on to computing inner. We
- have</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>[x1, x2, x3], [], [y1, y2, y3], [z1, z2]</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>as input and we need to output</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>[0, 0, 0, 2, 2, 2, 3, 3]</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>which is the concatenation of</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>[0, 0, 0], [], [2, 2, 2], [3, 3]</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Here each tuple is the same size as the input, but is filled with a constant
- that represents its index in the argument list. The first tuple is filled with
- 0, the second with 1, the third with 2, and so on.</p>
- </div>
- <div class="paragraph">
- <p>We can achieve this result if we first compute a list of indices, in our case
- <code>[0, 1, 2, 3]</code>, then use binary <code>mp_transform</code> on the two lists</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>[[x1, x2, x3], [], [y1, y2, y3], [z1, z2]]
- [0, 1, 2, 3]</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and a function which takes a list and an integer (in the form of an
- <code>std::integral_constant</code>) and returns a list that is the same size as the
- original, but filled with the second argument.</p>
- </div>
- <div class="paragraph">
- <p>We’ll call this function <code>mp_fill</code>, after <code>std::fill</code>.</p>
- </div>
- <div class="paragraph">
- <p>Functional programmers will immediately realize that <code>mp_fill</code> is
- <code>mp_transform</code> with a function that returns a constant, and here’s an
- implementation along these lines:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class V> struct mp_constant
- {
- template<class...> using apply = V;
- };
- template<class L, class V>
- using mp_fill = mp_transform<mp_constant<V>::template apply, L>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Here’s an alternate implementation:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class L, class V> struct mp_fill_impl;
- template<template<class...> class L, class... T, class V>
- struct mp_fill_impl<L<T...>, V>
- {
- template<class...> using _fv = V;
- using type = L<_fv<T>...>;
- };
- template<class L, class V> using mp_fill = typename mp_fill_impl<L, V>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>These demonstrate different styles and choosing one over the other is largely a
- matter of taste here. In the first case, we combine existing primitives; in the
- second case, we "inline" <code>mp_const</code> and even <code>mp_transform</code> in the body of
- <code>mp_fill_impl</code>.</p>
- </div>
- <div class="paragraph">
- <p>Most C++11 programmers will probably find the second implementation easier to
- read.</p>
- </div>
- <div class="paragraph">
- <p>We can now <code>mp_fill</code>, but we still need the <code>[0, 1, 2, 3]</code> index sequence. We
- could write an algorithm <code>mp_iota</code> for that (named after
- <a href="http://en.cppreference.com/w/cpp/algorithm/iota"><code>std::iota</code></a>), but it so
- happens that C++14 already has a standard way of generating an index
- sequence, called
- <a href="http://en.cppreference.com/w/cpp/utility/integer_sequence"><code>std::make_index_sequence</code></a>.
- Since Eric’s original solution makes use of <code>make_index_sequence</code>, let’s follow
- his lead.</p>
- </div>
- <div class="paragraph">
- <p>Technically, this takes us outside of C++11, but <code>make_index_sequence</code> is not
- hard to implement (if efficiency is not a concern):</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class T, T... Ints> struct integer_sequence
- {
- };
- template<class S> struct next_integer_sequence;
- template<class T, T... Ints> struct next_integer_sequence<integer_sequence<T, Ints...>>
- {
- using type = integer_sequence<T, Ints..., sizeof...(Ints)>;
- };
- template<class T, T I, T N> struct make_int_seq_impl;
- template<class T, T N>
- using make_integer_sequence = typename make_int_seq_impl<T, 0, N>::type;
- template<class T, T I, T N> struct make_int_seq_impl
- {
- using type = typename next_integer_sequence<
- typename make_int_seq_impl<T, I+1, N>::type>::type;
- };
- template<class T, T N> struct make_int_seq_impl<T, N, N>
- {
- using type = integer_sequence<T>;
- };
- template<std::size_t... Ints>
- using index_sequence = integer_sequence<std::size_t, Ints...>;
- template<std::size_t N>
- using make_index_sequence = make_integer_sequence<std::size_t, N>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>We can now obtain an <code>index_sequence<0, 1, 2, 3></code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... Tp,
- class R = mp_append<std::tuple<>, typename std::remove_reference<Tp>::type...>>
- R tuple_cat( Tp &&... tp )
- {
- std::size_t const N = sizeof...(Tp);
- // inner
- using seq = make_index_sequence<N>;
- }</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>but <code>make_index_sequence<4></code> returns <code>integer_sequence<std::size_t, 0, 1, 2,
- 3></code>, which is not a type list. In order to work with it, we need to convert it
- to a type list, so we’ll introduce a function <code>mp_from_sequence</code> that does
- that.</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class S> struct mp_from_sequence_impl;
- template<template<class T, T... I> class S, class U, U... J>
- struct mp_from_sequence_impl<S<U, J...>>
- {
- using type = mp_list<std::integral_constant<U, J>...>;
- };
- template<class S> using mp_from_sequence = typename mp_from_sequence_impl<S>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>We can now compute the two lists that we wanted to transform with <code>mp_fill</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... Tp,
- class R = mp_append<std::tuple<>, typename std::remove_reference<Tp>::type...>>
- R tuple_cat( Tp &&... tp )
- {
- std::size_t const N = sizeof...(Tp);
- // inner
- using list1 = mp_list<typename std::remove_reference<Tp>::type...>;
- using list2 = mp_from_sequence<make_index_sequence<N>>;
- // list1: [[x1, x2, x3], [], [y1, y2, y3], [z1, z2]]
- // list2: [0, 1, 2, 3]
- return R{};
- }</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and finish the job of computing <code>inner</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... Tp,
- class R = mp_append<std::tuple<>, typename std::remove_reference<Tp>::type...>>
- R tuple_cat( Tp &&... tp )
- {
- std::size_t const N = sizeof...(Tp);
- // inner
- using list1 = mp_list<typename std::remove_reference<Tp>::type...>;
- using list2 = mp_from_sequence<make_index_sequence<N>>;
- // list1: [[x1, x2, x3], [], [y1, y2, y3], [z1, z2]]
- // list2: [0, 1, 2, 3]
- using list3 = mp_transform<mp_fill, list1, list2>;
- // list3: [[0, 0, 0], [], [2, 2, 2], [3, 3]]
- using inner = mp_rename<list3, mp_append>; // or mp_apply<mp_append, list3>
- // inner: [0, 0, 0, 2, 2, 2, 3, 3]
- return R{};
- }</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>For <code>outer</code>, we again have</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>[x1, x2, x3], [], [y1, y2, y3], [z1, z2]</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>as input and we need to output</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>[0, 1, 2, 0, 1, 2, 0, 1]</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>which is the concatenation of</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>[0, 1, 2], [], [0, 1, 2], [0, 1]</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>The difference here is that instead of filling the tuple with a constant value,
- we need to fill it with increasing values, starting from 0, that is, with the
- result of <code>make_index_sequence<N></code>, where <code>N</code> is the number of elements.</p>
- </div>
- <div class="paragraph">
- <p>The straightforward way to do that is to just define a metafunction <code>F</code> that
- does what we want, then use <code>mp_transform</code> to apply it to the input:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class N> using mp_iota = mp_from_sequence<make_index_sequence<N::value>>;
- template<class L> using F = mp_iota<mp_size<L>>;
- template<class... Tp,
- class R = mp_append<std::tuple<>, typename std::remove_reference<Tp>::type...>>
- R tuple_cat( Tp &&... tp )
- {
- std::size_t const N = sizeof...(Tp);
- // outer
- using list1 = mp_list<typename std::remove_reference<Tp>::type...>;
- using list2 = mp_transform<F, list1>;
- // list2: [[0, 1, 2], [], [0, 1, 2], [0, 1]]
- using outer = mp_rename<list2, mp_append>;
- // outer: [0, 1, 2, 0, 1, 2, 0, 1]
- return R{};
- }</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Well that was easy. Surprisingly easy. The one small annoyance is that we can’t
- define <code>F</code> inside <code>tuple_cat</code> - templates can’t be defined in functions.</p>
- </div>
- <div class="paragraph">
- <p>Let’s put everything together.</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class N> using mp_iota = mp_from_sequence<make_index_sequence<N::value>>;
- template<class L> using F = mp_iota<mp_size<L>>;
- template<class R, class...Is, class... Ks, class Tp>
- R tuple_cat_( mp_list<Is...>, mp_list<Ks...>, Tp tp )
- {
- return R{ std::get<Ks::value>(std::get<Is::value>(tp))... };
- }
- template<class... Tp,
- class R = mp_append<std::tuple<>, typename std::remove_reference<Tp>::type...>>
- R tuple_cat( Tp &&... tp )
- {
- std::size_t const N = sizeof...(Tp);
- // inner
- using list1 = mp_list<typename std::remove_reference<Tp>::type...>;
- using list2 = mp_from_sequence<make_index_sequence<N>>;
- // list1: [[x1, x2, x3], [], [y1, y2, y3], [z1, z2]]
- // list2: [0, 1, 2, 3]
- using list3 = mp_transform<mp_fill, list1, list2>;
- // list3: [[0, 0, 0], [], [2, 2, 2], [3, 3]]
- using inner = mp_rename<list3, mp_append>; // or mp_apply<mp_append, list3>
- // inner: [0, 0, 0, 2, 2, 2, 3, 3]
- // outer
- using list4 = mp_transform<F, list1>;
- // list4: [[0, 1, 2], [], [0, 1, 2], [0, 1]]
- using outer = mp_rename<list4, mp_append>;
- // outer: [0, 1, 2, 0, 1, 2, 0, 1]
- return tuple_cat_<R>( inner(), outer(),
- std::forward_as_tuple( std::forward<Tp>(tp)... ) );
- }</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>This almost compiles, except that our <code>inner</code> happens to be a <code>std::tuple</code>, but
- our helper function expects an <code>mp_list</code>. (<code>outer</code> is already an <code>mp_list</code>, by
- sheer luck.) We can fix that easily enough.</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>return tuple_cat_<R>( mp_rename<inner, mp_list>(), outer(),
- std::forward_as_tuple( std::forward<Tp>(tp)... ) );</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Let’s define a <code>print_tuple</code> function and see if everything checks out.</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<int I, int N, class... T> struct print_tuple_
- {
- void operator()( std::tuple<T...> const & tp ) const
- {
- using Tp = typename std::tuple_element<I, std::tuple<T...>>::type;
- print_type<Tp>( " ", ": " );
- std::cout << std::get<I>( tp ) << ";";
- print_tuple_< I+1, N, T... >()( tp );
- }
- };
- template<int N, class... T> struct print_tuple_<N, N, T...>
- {
- void operator()( std::tuple<T...> const & ) const
- {
- }
- };
- template<class... T> void print_tuple( std::tuple<T...> const & tp )
- {
- std::cout << "{";
- print_tuple_<0, sizeof...(T), T...>()( tp );
- std::cout << " }\n";
- }
- int main()
- {
- std::tuple<int, long> t1{ 1, 2 };
- std::tuple<> t2;
- std::tuple<float, double, long double> t3{ 3, 4, 5 };
- std::pair<void const*, char const*> t4{ "pv", "test" };
- using expected = std::tuple<int, long, float, double, long double,
- void const*, char const*>;
- auto result = ::tuple_cat( t1, t2, t3, t4 );
- static_assert( std::is_same<decltype(result), expected>::value, "" );
- print_tuple( result );
- }</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Output:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>{ int: 1; long: 2; float: 3; double: 4; long double: 5; void const*: 0x407086;
- char const*: test; }</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Seems to work. But there’s at least one error left. To see why, replace the
- first tuple</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>std::tuple<int, long> t1{ 1, 2 };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>with a pair:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>std::pair<int, long> t1{ 1, 2 };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>We now get an error at</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>using inner = mp_rename<list3, mp_append>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>because the first element of <code>list3</code> is an <code>std::pair</code>, which <code>mp_append</code> tries
- and fails to use as its return type.</p>
- </div>
- <div class="paragraph">
- <p>There are two ways to fix that. The first one is to apply the same trick we
- used for the return type, and insert an empty <code>mp_list</code> at the front of
- <code>list3</code>, which <code>mp_append</code> will use as a return type:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>using inner = mp_rename<mp_push_front<list3, mp_list<>>, mp_append>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>The second way is to just convert all inputs to mp_list:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>using list1 = mp_list<
- mp_rename<typename std::remove_reference<Tp>::type, mp_list>...>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>In both cases, inner will now be an <code>mp_list</code>, so we can omit the <code>mp_rename</code>
- in the call to <code>tuple_cat_</code>.</p>
- </div>
- <div class="paragraph">
- <p>We’re done. The results hopefully speak for themselves.</p>
- </div>
- </div>
- </div>
- <div class="sect1">
- <h2 id="higher_order_metaprogramming_or_lack_thereof">Higher order metaprogramming, or lack thereof</h2>
- <div class="sectionbody">
- <div class="paragraph">
- <p>Perhaps by now you’re wondering why this article is called "Simple C++11
- metaprogramming", since what we covered so far wasn’t particularly simple.</p>
- </div>
- <div class="paragraph">
- <p>The <em>relative</em> simplicity of our approach stems from the fact that we’ve not
- been doing any higher order metaprogramming, that is, we haven’t introduced any
- primitives that return metafunctions, such as <code>compose</code>, <code>bind</code>, or a lambda
- library.</p>
- </div>
- <div class="paragraph">
- <p>I posit that such higher order metaprogramming is, in the majority of cases,
- not necessary in C++11. Consider, for example, Eric Niebler’s solution given
- above:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>using outer =
- typelist_cat_t<
- typelist_transform_t<
- typelist<as_typelist_t<Tuples>...>,
- meta_compose<
- meta_quote<as_typelist_t>,
- meta_quote_i<std::size_t, make_index_sequence>,
- meta_quote<typelist_size_t> > > >;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>The <code>meta_compose</code> expression takes three other ("quoted") metafunctions and
- creates a new metafunction that applies them in order. Eric uses this example
- as motivation to introduce the concept of a "metafunction class" and then to
- supply various primitives that operate on metafunction classes.</p>
- </div>
- <div class="paragraph">
- <p>But when we have metafunctions <code>F</code>, <code>G</code> and <code>H</code>, instead of using
- <code>meta_compose</code>, in C++11 we can just do</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... T> using Fgh = F<G<H<T...>>>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>and that’s it. The language makes defining composite functions easy, and there
- is no need for library support. If the functions to be composed are
- <code>as_typelist_t</code>, <code>std::make_index_sequence</code> and <code>typelist_size_t</code>, we just
- define</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... T>
- using F = as_typelist_t<std::make_index_sequence<typelist_size_t<T...>::value>>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Similarly, if we need a metafunction that will return <code>sizeof(T) < sizeof(U)</code>,
- there is no need to enlist a metaprogramming lambda library as in</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>lambda<_a, _b, less<sizeof_<_a>, sizeof_<_b>>>></code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>We could just define it inline:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class T, class U> using sizeof_less = mp_bool<(sizeof(T) < sizeof(U))>;</code></pre>
- </div>
- </div>
- </div>
- </div>
- <div class="sect1">
- <h2 id="one_more_thing">One more thing</h2>
- <div class="sectionbody">
- <div class="paragraph">
- <p>Finally, let me show the implementations of <code>mp_count</code> and <code>mp_count_if</code>, for
- no reason other than I find them interesting. <code>mp_count<L, V></code> returns the
- number of occurrences of the type <code>V</code> in the list <code>L</code>; <code>mp_count_if<L, P></code>
- counts the number of types in <code>L</code> for which <code>P<T></code> is <code>true</code>.</p>
- </div>
- <div class="paragraph">
- <p>As a first step, I’ll implement <code>mp_plus</code>. <code>mp_plus</code> is a variadic (not just
- binary) metafunction that returns the sum of its arguments.</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class... T> struct mp_plus_impl;
- template<class... T> using mp_plus = typename mp_plus_impl<T...>::type;
- template<> struct mp_plus_impl<>
- {
- using type = std::integral_constant<int, 0>;
- };
- template<class T1, class... T> struct mp_plus_impl<T1, T...>
- {
- static constexpr auto _v = T1::value + mp_plus<T...>::value;
- using type = std::integral_constant<
- typename std::remove_const<decltype(_v)>::type, _v>;
- };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>Now that we have <code>mp_plus</code>, <code>mp_count</code> is just</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class L, class V> struct mp_count_impl;
- template<template<class...> class L, class... T, class V>
- struct mp_count_impl<L<T...>, V>
- {
- using type = mp_plus<std::is_same<T, V>...>;
- };
- template<class L, class V> using mp_count = typename mp_count_impl<L, V>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>This is another illustration of the power of parameter pack expansion. It’s a
- pity that we can’t use pack expansion in <code>mp_plus</code> as well, to obtain</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>T1::value + T2::value + T3::value + T4::value + ...</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>directly. It would have been nice for <code>T::value + ...</code> to have been
- supported, and it appears that in C++17, it will be.</p>
- </div>
- <div class="paragraph">
- <p><code>mp_count_if</code> is similarly straightforward:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class L, template<class...> class P> struct mp_count_if_impl;
- template<template<class...> class L, class... T, template<class...> class P>
- struct mp_count_if_impl<L<T...>, P>
- {
- using type = mp_plus<P<T>...>;
- };
- template<class L, template<class...> class P>
- using mp_count_if = typename mp_count_if_impl<L, P>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>at least if we require <code>P</code> to return <code>bool</code>. If not, we’ll have to coerce
- <code>P<T>::value</code> to 0 or 1, or the count will not be correct.</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<bool v> using mp_bool = std::integral_constant<bool, v>;
- template<class L, template<class...> class P> struct mp_count_if_impl;
- template<template<class...> class L, class... T, template<class...> class P>
- struct mp_count_if_impl<L<T...>, P>
- {
- using type = mp_plus<mp_bool<P<T>::value != 0>...>;
- };
- template<class L, template<class...> class P>
- using mp_count_if = typename mp_count_if_impl<L, P>::type;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>The last primitive I’ll show is <code>mp_contains</code>. <code>mp_contains<L, V></code> returns
- whether the list <code>L</code> contains the type <code>V</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class L, class V> using mp_contains = mp_bool<mp_count<L, V>::value != 0>;</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>At first sight, this implementation appears horribly naive and inefficient — why would we need to count all the occurrences just to throw that away if we’re
- only interested in a boolean result — but it’s actually pretty competitive and
- perfectly usable. We just need to add one slight optimization to <code>mp_plus</code>, the
- engine behind <code>mp_count</code> and <code>mp_contains</code>:</p>
- </div>
- <div class="listingblock">
- <div class="content">
- <pre class="highlight"><code>template<class T1, class T2, class T3, class T4, class T5,
- class T6, class T7, class T8, class T9, class T10, class... T>
- struct mp_plus_impl<T1, T2, T3, T4, T5, T6, T7, T8, T9, T10, T...>
- {
- static constexpr auto _v = T1::value + T2::value + T3::value + T4::value +
- T5::value + T6::value + T7::value + T8::value + T9::value + T10::value +
- mp_plus<T...>::value;
- using type = std::integral_constant<
- typename std::remove_const<decltype(_v)>::type, _v>;
- };</code></pre>
- </div>
- </div>
- <div class="paragraph">
- <p>This cuts the number of template instantiations approximately tenfold.</p>
- </div>
- </div>
- </div>
- <div class="sect1">
- <h2 id="conclusion">Conclusion</h2>
- <div class="sectionbody">
- <div class="paragraph">
- <p>I have outlined an approach to metaprogramming in C++11 that</p>
- </div>
- <div class="ulist">
- <ul>
- <li>
- <p>takes advantage of variadic templates, parameter pack expansion, and template
- aliases;</p>
- </li>
- <li>
- <p>operates on any variadic template <code>L<T...></code>, treating it as its
- fundamental data structure, without mandating a specific type list
- representation;</p>
- </li>
- <li>
- <p>uses template aliases as its metafunctions, with the expression <code>F<T...></code>
- serving as the equivalent of a function call;</p>
- </li>
- <li>
- <p>exploits the structural similarity between the data structure <code>L<T...></code>
- and the metafunction call <code>F<T...></code>;</p>
- </li>
- <li>
- <p>leverages parameter pack expansion as much as possible, instead of using the
- traditional recursive implementations;</p>
- </li>
- <li>
- <p>relies on inline definitions of template aliases for function composition,
- instead of providing library support for this task.</p>
- </li>
- </ul>
- </div>
- </div>
- </div>
- <div class="sect1">
- <h2 id="further_reading">Further reading</h2>
- <div class="sectionbody">
- <div class="paragraph">
- <p><a href="simple_cxx11_metaprogramming_2.html">Part 2 is now available</a>, in which I
- show algorithms that allow us to treat type lists as sets, maps, and vectors,
- and demonstrate various C++11 implementation techniques in the process.</p>
- </div>
- </div>
- </div>
- </div>
- <div id="footer">
- <div id="footer-text">
- Last updated 2019-12-10 00:19:27 UTC
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