## Functional compile-time templates based type lists in C++

Hi,

Have you ever heard about typelists in C++ ? That just consists in using the functional way of defining lists, but with templates.

It looks like that :

template <typename Head, typename Tail> struct TypeList { typedef Head head; typedef Tail tail; };

However, we’ll need a type representing an empty type list. Ours will be the following.

struct EmptyList { };

How to write metafunctions (compile-time functions, working over types and not values — actually, the types are in this context like “values”) for these type lists now ?

Let’s start with a metafunction computing the length of a type list :

// declaration template <typename Typelist> struct Length; // the normal case : the head element of the list (it's a type), and the tail, which is itself a type list template <typename H, typename T> struct Length<TypeList<H, T> > { static const int value = 1 + Length<T>::value ; }; // the terminal case : our typelist is the empty list, we're at the end of the list, so we won't add 1 neither we will go on with the recursion template <> struct Length<EmptyList> { static const int value = 0 ; };

Now, calling it on a given typelist will return us the good result :

Length< TypeList<int, TypeList<char, TypeList<bool, EmptyList> > > >::value // equals 3

Do you want more ? I guess you do, of course. Let’s tackle a more complicated one : Map. It maps a type list to another one, computing the result of the application of a metafunction on each type of the type list. Ok, let’s start with the declaration.

template <typename TL, template <typename> class Func> struct Map;

Now, the basical case, with a head element and the tail, will consist in computing the result of the application of the metafunction of the head element, and appending to it the result of Map on the tail. Looks like that :

template <typename H, typename T, template <typename> class Func> struct Map<TypeList<H, T>, Func> { typedef TypeList< typename Func<H>::type, typename Map<T, Func>::type > type; };

And the trivial case, on the empty list :

template <template <typename> class Func> struct Map<EmptyList, Func> { typedef EmptyList type; };

And we’re done with Map !

Let’s see one more interesting function over type lists : Filter. It’ll filter (really ?!) the type list according to a compile-time predicate, and return the original type list without the types that didn’t match the predicate.

Here we go !

template <typename TypeList, template <typename> class Pred> struct Filter; template <typename H, typename T, template <typename> class Pred, bool result> struct FilterAux { typedef typename Filter<T, Pred>::type type; }; template <typename H, typename T, template <typename> class Pred> struct FilterAux<H, T, Pred, true> { typedef TypeList<H, typename Filter<T, Pred>::type> type; }; template <typename H, typename T, template <typename> class Pred> struct Filter<TypeList<H, T>, Pred> { typedef typename FilterAux<H, T, Pred, Pred<H>::value>::type type; }; template <template <typename> class Pred> struct Filter<EmptyList, Pred> { typedef EmptyList type; };

This one was trickier, because we needed an auxiliary template structure to have a bool against which we could specialize, to either go on without keeping the type in the type list (in case it doesn’t match the predicate) or keeping it.

Now, I’ll leave as exercise the following functions :

- Repeat : takes a type, a number, and returns a type list containing n times the given type

- Take : takes a type list and a number, and returns a type list contaning the first n elements of the typelist if possible, less otherwise.

- Interleave : it takes 2 two lists, say l1 = [T1, T2, T3] and l2 = [U1, U2, U3] and returns the list [T1, U1, T2, U2, T3, U3]

- Zip : takes two lists and returns a list of component-wise pairs of the types

- ZipWith : takes two lists and a function itself taking two types and returning a type, and returns a list compound of the component-wise application of the given function on both lists simultaneously

I’ll try to post these during the upcoming days.

Good functional metaprogramming to all ;)

## Why expression templates matter ?

Imagine we are using a matrix library, with a naive implementation of +, that simply adds column and row-wise each coefficient. Thus, for a, m1, m2, m3 being for example square matrices of order n, if we want to compute the sum of m1, m2 and m3 and to put the result in a, corresponding to the following code :

a = m1 + m2 + m3

then the computation will look like the following tree :

Thus, there will be a first for loop to compute *m1 + m2* which will result in a matrix we’ll call *t*, then another one to compute *t + m3*. For 3×3 matrices, it’s ok. Imagine n is actually 40000. Doing two for loops of 40000 iterations where we would do a single one… quite annoying, isn’t it ? Actually, we would rather want an evaluation tree like the following :

Here comes expression templates ;)

It’ll need a bit of refactoring though. First, let’s say our matrix type is the following (we’ll only deal with float to avoid ambedding an additional typename template parameter representing the number type we use) :

template <unsigned int N> class matrix { float data[N*N]; public: float operator()(unsigned int row, unsigned int col) const { return data[row + N*col]; } float& operator()(unsigned int row, unsigned int col) { return data[row + N*col]; } }; template <unsigned int N> std::ostream & operator<<(std::ostream& o, const matrix<N>& m) { o << "["; for(unsigned int row = 0; row < N; row++) { for(unsigned int col = 0; col < N; col++) { o << m(row,col); if(col != N-1) o << ";"; } if(row != N-1) o << "\n"; } o << "]"; return o; }

Now, we’ll have to define a **Domain Specific Embedded Language** for matrix operations. Like in any language people design, we will have a tree representing what’s happening in the code. In our case, it’ll represent the evaluation tree of the matrix operations we’re dealing with. Thus, like in any expression tree, we need an *Expression* type. Ours will look like this :

template <typename LeftOperandType, typename OperationTag, typename RightOperandType> struct Expression { const LeftOperandType& l; const RightOperandType& r; Expression(const LeftOperandType& l_, const RightOperandType& r_) : l(l_), r(r_) { } float operator() (unsigned int row, unsigned int col) const { return OperationTag::apply(l(row, col), r(row,col)); } };

Ok, now, what should an *OperationTag* look like ? Well, we’ll implement the operation tag corresponding to additions :

struct plus { static float apply(float a, float b) { return a+b; } };

and the *+ operator* that’ll let us create an expression with a ‘plus’ operation.

template <typename L, typename R> Expression<L, plus, R> operator+(const L& l, const R& r) { return Expression<L, plus, R>(l, r); }

Thanks to the definition of *Expression*, we can embed matrix operations in Expressions, but for the moment we can’t do the reverse way, that is we can’t convert an *Expression* to a *matrix*. So let’s write an *operator=* in the *matrix* class.

// inside the matrix class template <typename ExprType> matrix<N>& operator=(const ExprType& e) { for(unsigned int row = 0; row < N; row++) { for(unsigned int col = 0; col < N; col++) { (*this)(row, col) = e(row, col); } } return (*this); }

So you see, this is the only moment where we call the *operator()(unsigned int, unsigned int)* of the *Expression* type. Thus, this is the only moment when the whole expression is being evaluated. Let’s study the following code.

#include <iostream> #include "matrix.h" #include "expression.h" int main() { matrix<2> m1; m1(0,0) = 1.0; m1(1,0) = 0.0; m1(0,1) = 4.0; m1(1,1) = 1.0; matrix<2> m2; m2(0,0) = 0.0; m2(1,0) = -1.0; m2(0,1) = 1.0; m2(1,1) = 2.0; matrix<2> m3; m3(0,0) = 1.0; m3(1,0) = -2.0; m3(0,1) = 3.0; m3(1,1) = 5.0; matrix<2> a; a = m1 + m2 + m3; std::cout << a << std::endl; }

Here, “m1 + m2 + m3″ crates an

Expression< Expression<matrix<2>, plus, matrix<2> >, plus, matrix<2> >

instance. The coefficients aren’t computed until *operator=* is called. Indeed, we have the following expression tree.

That is, we know which operations we have to call, on which matrices, but nothing is evaluated. The only place where we call *operator() (unsigned int, unsigned int)* on a value of type *Expression* is in *matrix<N>::operator=*, and this call actually computes each coefficient, one by one, applying the whole computation tree (here, two calls to ‘+’) for each coefficient. This way, we only execute the two for loops once, and it’ll remain the same whatever the number of computations is. Moreover, the only change we had to make to our matrix class was to add an operator= to be able to assign an expression to a matrix.

By the way, the output of our main function is the following.

[2;8

-3;8]

I hope you enjoyed this post ;)

## Templates for unique id generation for types : a beginning

After reading one of the comments on this blog post, I decided to publish here a proof of concept for the generation of unique ids for types.

Basically, it’s just about one template structure, using very basical templates techniques : specialization, metaprogramming-level recursion and nested enum for the computation. Either a familiarity with template metaprogramming or with functional programming is enough to understand the following code.

If you’re familiar with any scheme of functional recursion, or recursion in its mathematical sense, you’ll get it quite easily. Mathematically, we’re somehow defining a recursive function *generate_id* this way :

Which, in C++, becomes :

template <typename T> struct id_generator; template <typename T> struct id_generator<T*> { enum { result = id_generator<T>::result*2 }; }; template <typename T> struct id_generator<T&> { enum { result = id_generator<T>::result*3 }; }; template <typename T> struct id_generator< std::vector<T> > { enum { result = id_generator<T>::result*11 }; }; template <> struct id_generator<int> { enum { result = 5 }; }; template <> struct id_generator<char> { enum { result = 7 }; };

And a minimal example of use :

int main() { std::cout << "int : " << id_generator< int >::result << std::endl << "char**** : " << id_generator< char**** >::result << std::endl << "vector<int> : " << id_generator< std::vector<int> >::result << std::endl; return 0; } /* Output : int : 5 char**** : 112 vector<int> : 55 */

To make it really usable, you’ll have to add much (much much much) more :

- base types, like int and char here, which help for terminating the recursive call
- composition rules, like vector, references and pointers here, which help for propagating the recursion

To ensure the uniqueness here, I use prime numbers, simply [1]. Indeed, for the base types, I give a value being a prime number. For the different compositions, I multiply by a different prime number for each. However, most of you may have noticed that the id only lets you know about what type compositions and base types are used, but gives nothing about the order. If we add a rule for std::list, multiplying by 13 for example, then *a list of vectors of ints* will have the same id as *a vector of lists of int*. It’d need additional code and workarounds to take the order of the compositions in account — I guess it is possible though. If any reader here comes up with a solution, let us know. A possible solution would be to drop prime numbers, since they rely on a commutative (abelian) ring [2].

[1] http://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic

[2] http://en.wikipedia.org/wiki/Commutative_ring

## Introduction to SFINAE

Basically, SFINAE (for the smart guys who can remember the whole name : *Substitution Failure Is Not An Error*) is what makes this code compile.

struct Test { typedef int type; }; template < typename T > void f( typename T::type ) {} // definition #1 template < typename T > void f( T ) {} // definition #2 f< Test > ( 10 ); // calls #1 f< int > ( 10 ); //calls #2 without error, thanks to SFINAE

To make it short (but not too much), if you have several overloads for a function, but particularly one of them being template, then if the template one doesn’t match the call you’re currently doing, the compiler — instead of raising a bright, clear and boring error — will try the other ones. In our case, the first definition of **f** asks for the type parameter to have a nested *type* type defined (either via class, struct, enum or typedef). Fortunately, *Test* has one ! But our lonely *int* type hasn’t. Again, fortunately, the compiler, thanks to SFINAE, will not issue an error and will call *#2*.

Ok, you got it, but now wonder how can this be useful ? Okay, imagine we basically are working on a widget library. After a huge amount of work, we came up with the following code :

class label { }; class button { };

Yeah, impressive, isn’t it ?

Okay, now, say we want to write *show* functions, to be able to show our two widgets. Basically, we can just write two overloads. But it’ll base the overload resolution on the strict name of the type. What if we rather want the overload resolution to be done using the structure of our type ? For example, depending on the presence of a ‘label_tag’ inner typedef, or ‘button_tag’, for button.

Then,, first, we’d modify our two classes this way :

class label { public: typedef void label_tag; }; class button { public: typedef void button_tag; };

Then, how can we apply the SFINAE principle here ? Well, here is one way :

template <typename widget_type> typename widget_type::label_tag show(widget_type& w) { std::cout<< "I'm a label" << std::endl; } template <typename widget_type> typename widget_type::button_tag show(widget_type& w) { std::cout << "I'm a button" << std::endl; }

And then, the main function and its output :

int main() { label l; button b; show(l); show(b); return 0; } /* Output : * I'm a label * I'm a button */

Got it ? ;)

Maybe I’ll dive into more advanced uses of SFINAE (more complex and powerful interface detection) in further posts.

Stay tuned !

## Can I haz teh boost::any C++ class plz ?

Welcome,

This blog post will be about rewriting the boost::any class. For those of you who don’t know it, it lets you assign a value of any type to your *boost::any* instance, like in the following code :

boost::any a = 42; a = "C++"; a = 3.14; // and so on

First, ok, we must have templates somewhere, since there isn’t any base class of all the possible types, even less when we deal with primitive types. So, our *any* cass must hold a value than actually can hold any kind of stuffs… Some value_type template class then ! But wait, we must be able to store value_type<int>, value_type<std::string> and so on ! OK, fortunately, **type erasure** will save us here. We’ll create a base class *value_base* and then make a template class value_type inherit it.

class value_base { public: virtual ~value_base() { } }; template <class T> class value_type : public value_base { T t; public: value_type(const T& t_) : t(t_) { } };

Thus, we can write the any class this way :

class any { value_base* v; public: any() : v(0) { } template <class value_t> any(const value_t& v_) : v(new value_type<value_t>(v_)) { } ~any() { delete v; } };

Ok, now we miss a copy constructor and an overload for the “=” operator.

We must first add a cloning function in value_base (pure virtual) and value_type for being able to write a good copy constructor.

class value_base { public: virtual ~value_base() { } virtual value_base* clone() const = 0; /* new */ }; template <class T> class value_type : public value_base { T t; public: value_type(const T& t_) : t(t_) { } value_base* clone() const /* new */ { return new value_type(t); } };

And now, *any(const any&)* and *any& operator=(const any&)* can be implemented ;)

class any { value_base* v; public: any() : v(0) { } template <class value_t> any(const value_t& v_) : v(new value_type<value_t>(v_)) { } /* new */ any(any const & other) : v(other.v ? other.v->clone() : 0) {} /* new */ any& operator=(const any& other) { if(&other != this) { any copy(other); swap(copy); } return *this; } /* new */ void swap(any& other) { std::swap(v, other.v); } ~any() { delete v; } };

And you’re done !

For those of you who either already knew any or just read a bit its documentation, you may be interested in the any cast functions, that let you get back a value from an *any* instance. Here is the code (it requires very little modifications to our previous code).

class any; template <class T> T any_cast(any& a); // declaration for being able to make classes friend of it // value_type template class modification template <class T> class value_type : public value_base { friend T any_cast<>(any& a); // ... }; // any class modification class any { template <class T> friend T any_cast(any& a); // ... }; // bad_any_cast exception class class bad_any_cast : public std::exception { public: const char* what() const throw() { return "Bad any_cast exception"; } }; template <class T> T any_cast(any& a) { value_type<T>* v = dynamic_cast<value_type<T>*>(a.v); if(v == 0) { throw bad_any_cast(); } else { return v->t; } }

I haven’t implemented all the cast functions. The ones with constant reference, pointer, and constant pointer are left as exercise for the reader.

Here is a code using all the things we’ve done so far.

int main() { any a = 42; any b = 'c'; std::cout << "[1] a=" << any_cast<int>(a) << " b='" << any_cast<char>(b) << "'" << std::endl; a.swap(b); std::cout << "[2] a='" << any_cast<char>(a) << "' b=" << any_cast<int>(b) << std::endl; try { std::string s = any_cast<std::string>(b); } catch(const std::exception& e) { std::cout << "[3] " << e.what() << std::endl; } any c(a); std::cout << "[4] c='" << any_cast<char>(c) << "'" << std::endl; return 0; } /* alp@mestan:~/cpp$ g++ -o te3 type_erasure3.cpp alp@mestan:~/cpp$ ./te3 [1] a=42 b='c' [2] a='c' b=42 [3] Bad any_cast exception [4] c='c' */

Enjoy ;)

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