Chapter 22: Class Templates

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Templates can not only be constructed for functions but also for complete classes. Consider constructing a class template when a class should be able to handle different types of data. Class templates are frequently used in C++: chapter 12 discusses data structures like vector, stack and queue, that are implemented as class templates. With class templates, the algorithms and the data on which the algorithms operate are completely separated from each other. To use a particular data structure in combination with a particular data type only the data type needs to be specified when defining or declaring a class template object (as in stack<int> iStack).

In this chapter constructing and using class templates is discussed. In a sense, class templates compete with object oriented programming (cf. chapter 14), that uses a mechanism resembling that of templates. Polymorphism allows the programmer to postpone the implementation of algorithms by deriving classes from base classes in which algorithms are only partially implemented. The actual definition and processing of the data upon which the algorithms operate may be postponed until derived classes are defined. Likewise, templates allow the programmer to postpone the specification of the data upon which the algorithms operate. This is most clearly seen with abstract containers, which completely specify the algorithms and at the same time leave the data type on which the algorithms operate completely unspecified.

There exists an intriguing correspondence between the kind of polymorphism we've encountered in chapter 14 and certain uses of class templates. In their book C++ Coding Standards (Addison-Wesley, 2005) Sutter and Alexandrescu refer to static polymorphism and dynamic polymorphism. Dynamic polymorphism is what we use when overriding virtual members. Using vtables the function that is actually called depends on the type of object a (base) class pointer points at. Static polymorphism is encountered in the context of templates, and is discussed and compared to dynamic polymorphism in section 22.12.

Generally, class templates are easier to use than polymorphism. It is certainly easier to write stack<int> istack to create a stack of ints than to derive a new class Istack: public stack and to implement all necessary member functions defining a similar stack of ints using object oriented programming. On the other hand, for each different type for which an object of a class template is defined another, possibly complete class must be reinstantiated. This is not required in the context of object oriented programming where derived classes use, rather than copy, the functions that are already available in their base classes (but see also section 22.11).

Previously we've already used class templates. Objects like vector<int> vi and vector<string> vs are commonly used. The data types for which these templates are defined and instantiated are an inherent part of such container types. It is stressed that it is the combination of a class template type and its template parameter(s), rather than the mere class template's type that defines or generates a type. So vector<int> is a type as is vector<string>. Such types could very well be represented by typedefs: 

    typedef std::vector<int>         IntVector;
    typedef std::vector<std::string> StringVector;

    IntVector vi;
    StringVector vs;

22.1: Defining class templates

Having covered the construction of function templates, we're now ready for the next step: constructing class templates. Many useful class templates already exist. Rather than illustrating the construction of a class template by looking at an already existing class template the construction of another potentially useful new class template will be undertaken.

The new class implements a circular queue. A circular queue has a fixed number of max_size elements. New elements are inserted at its back and only its head and tail elements can be accessed. Only the head element can be removed from a circular queue. Once n elements have been appended the next element is inserted again at the queue's (physical) first position. The circular queue allows insertions until it holds max_size elements. As long as a circular queue contains at least one element elements may be removed from it. Trying to remove an element from an empty circular queue or to add another element to a full circular queue results in exceptions being thrown. In addition to other constructors a circular queue must offer a constructor initializing its objects for max_size elements. This constructor must make available the memory for the max_size elements but must not call those elements default constructors (hinting at the use of the placement new operator). A circular queue should offer value semantics as well as a move constructor.

Please note that in the above description the actual data type that is used for the circular queue is nowhere mentioned. This is a clear indication that our class could very well be defined as a class template. Alternatively, the class could be defined for some concrete data type which is then abstracted when converting the class to a class template.

The actual construction of a class template is provided in the next section, where the class template CirQue (circular queue) is developed.

22.1.1: Constructing the circular queue: CirQue

The construction of a class template is illustrated in this section. Here, we'll develop the class template CirQue (circular queue). This class template has one template type parameter, Data, representing the data type that is stored in the circular queue. The outline of the interface of this class template looks like this: 
    template<typename Data>
    class CirQue
    {
        // member declarations
    };
A class template's definition starts like a function template's definition: Once the CirQue class template has been defined it can be used to create all kinds of circular queues. As one of its constructors expects a size_t argument defining the maximum number of elements that can be stored in the circular queue, circular queues could be defined like this: 
    CirQue<int> cqi(10);            // max 10 ints
    CirQue<std::string> cqstr(30);  // max 30 strings
As noted in the introductory section of this chapter the combination of name of the class template and the data type for which it is instantiated defines a data type. Also note the similarity between defining a std::vector (of some data type) and a CirQue (of some data type).

Like std::map containers class templates may be defined with multiple template type parameters.

Back to CirQue. A CirQue must be capable of storing max_size Data elements. These elements are eventually stored in memory pointed at by a pointer Data *d_data, initially pointing to raw memory. New elements are added at the backside of the CirQue. A pointer Data *d_back is used to point to the location where the next element is going to be stored. Likewise, Data *d_front points to the location of the CirQue's first element. Two size_t data members are used to monitor the filling state of the CirQue: d_size represents the number of elements currently stored in the CirQue, d_maxSize represents the maximum number of elements that the CirQue can contain. Thus, the CirQue's data members are: 

    size_t d_size;
    size_t d_maxSize;
    Data *d_data;
    Data *d_front;
    Data *d_back;

22.1.2: Non-type parameters

Function template parameters are either template type parameters or template non-type parameters (actually, a third type of template parameter exists, the template template parameter, which is discussed in chapter 23 (section 23.4)).

Class templates may also define non-type parameters. Like the function template non-type parameters they must be (integral) constants whose values must be known at object instantiation time.

Different from function template non-type parameters the values of class template non-type parameters are not deduced by the compiler using arguments passed to class template members.

Assume we extend our design of the class template CirQue so that it defines a second (non-type) parameter size_t Size. Our intent is to use this Size parameter in the constructor defining an array parameter of Size elements of type Data.

The CirQue class template now becomes (only showing the relevant constructor): 

    template <typename Data, size_t Size>
    class CirQue
    {
        // ... data members
        public:
            CirQue(Data const (&arr)[Size]);
            ...
    };

    template <typename Data, size_t Size>
    CirQue<Data, Size>::CirQue(Data const (&arr)[Size])
    :
        d_maxSize(Size),
        d_size(0),
        d_data(operator new(Size * sizeof(Data))),
        d_front(d_data),
        d_back(d_data),
    {
        std::copy(arr, arr + Size, back_inserter(*this));
    }
Unfortunately, this setup doesn't satisfy our needs as the values of template non-type parameters are not deduced by the compiler. When the compiler is asked to compile the following main function it reports a mismatch between the required and actual number of template parameters: 
    int main()
    {
        int arr[30];

        CirQue<int> ap(arr);
    }
    /*
        Error reported by the compiler:

        In function `int main()':
            error: wrong number of template arguments (1, should be 2)
            error: provided for `template<class Data, size_t Size>
                   class CirQue'
    */
Defining Size as a non-type parameter having a default value doesn't work either. The compiler always uses the default unless its value is explicitly specified. Reasoning that Size can be 0 unless we need another value, we might be tempted to specify size_t Size = 0 in the template's parameter type list. Doing so we create a mismatch between the default value 0 and the actual size of the array arr as defined in the above main function. The compiler, using the default value, reports: 
    In instantiation of `CirQue<int, 0>':
    ...
    error: creating array with size zero (`0')
So, although class templates may use non-type parameters they must always be specified like type parameters when an object of that class is defined. Default values can be specified for those non-type parameters causing the compiler to use the default when the non-type parameter is left unspecified.

Default template parameter values (either type or non-type template parameters) may not be specified when defining template member functions. In general: function template definitions (and thus: class template member functions) may not be given default template (non) type arguments. If default template arguments are to be used for class template members, they have to be specified by the class interface.

Similar to non-type parameters of function templates default argument values for non-type class template parameters may only be specified as constants:

Although our attempts to define a constructor of the class CirQue accepting an array as its argument has failed so far, we're not yet out of options. In the next section a method is described that does allow us to reach our goal.

22.1.3: Member templates

Our previous attempt to define a template non-type parameter that is initialized by the compiler to the number of elements of an array failed because the template's parameters are not implicitly deduced when a constructor is called. Instead, they must explicitly be specified when an object of the class template is defined. As the template arguments are specified just before the template's constructor is called the compiler doesn't have to deduce anything and it can simply use the explicitly specified template arguments.

In contrast, when function templates are used, the actual template parameters are deduced from the arguments used when calling the function. This opens up an alley leading to the solution of our problem. If the constructor itself is turned into a function template (having its own template header), then the compiler will be able to deduce the non-type parameter's value and there is no need anymore to specify it explicitly using a class template non-type parameter.

Members (functions or nested classes) of class templates that are themselves templates are called member templates.

Member templates are defined as any other template, including its own template header.

When converting our earlier CirQue(Data const (&array)[Size]) constructor into a member template the class template's Data type parameter can still be used, but we must provide the member template with a non-type parameter of its own. Its declaration in the (partially shown) class interface looks like this: 

    template <typename Data>
    class CirQue
    {
        public:
            template <size_t Size>
            explicit CirQue(Data const (&arr)[Size]);
    };
Its implementation becomes: 
    template <typename Data>
    template <size_t Size>
    CirQue<Data>::CirQue(Data const (&arr)[Size])
    :
        d_size(0),
        d_maxSize(Size),
        d_data(static_cast<Data *>(operator new(sizeof(arr)))),
        d_front(d_data),
        d_back(d_data)
    {
        std::copy(arr, arr + Size, back_inserter(*this));
    }

The implementation uses the STL's copy algorithm and a back_inserter adapter to insert the array's elements into the CirQue. To use the back_inserter CirQue must define two (public) typedefs (cf. section 18.2.2): 

    typedef Data value_type;
    typedef value_type const &const_reference;

Member templates have the following characteristics:

A potentially occurring problem remains. Assume that in addition to the above member template a CirQue<Data>::CirQue(Data const *data) has been defined. Some (here not further elaborated) protocol could be defined allowing the constructor to determine the number of elements that should be stored in the CirQue object. When we now define 

    CirQue<int> object(array);
it is this latter constructor, rather than the member template, that the compiler will use.

The compiler selects this latter constructor as it is a more specialized version of a constructor of the class CirQue than the member template (cf. section 21.14). Problems like these can be solved by defining the constructor CirQue(Data const *data) into a member template as well or by defining a constructor using two parameters, the second parameter defining the number of elements to copy.

When using the former constructor (i.e., the member template) it must define a template type parameter Data2. Here `Data' cannot be used as template parameters of a member template may not shadow template parameters of its class. Using Data2 instead of Data takes care of this subtlety. The following declaration of the constructor CirQue(Data2 const *) could appear in CirQue's header file: 

    template <typename Data>
    class CirQue
    {
        template <typename Data2>
        explicit CirQue(Data2 const *data);
    }
Here is how the two constructors are selected in code defining two CirQue objects: 
    int main()
    {
        int array[30];
        int *iPtr = array;

        CirQue<int> ac(array);      // calls CirQue(Data const (&arr)[Size])
        CirQue<int> acPtr(iPtr);    // calls CirQue(Data2 const *)
    }

22.1.4: CirQue's constructors and member functions

It's time to return to Cirque's design and construction again.

The class CirQue offers various member functions. Normal design principles should be adhered to when constructing class template members. Class template type parameters should preferably be defined as Type const &, rather than Type, to prevent unnecessary copying of large data structures. Template class constructors should use member initializers rather than member assignment within the body of the constructors. Member function definitions should preferably not be provided in-class but below the class interface. Since class template member functions are function templates their definitions should be provided in the header file offering the class interface. They may be given the inline attribute.

CirQue declares several constructors and (public) members (their definitions are provided as well; all definitions are provided below the class interface).

Here are the constructors and the destrctor:

Here are Cirque's members:

The remaining public members all consist of one-liners and were implemented as inline function templates:

Finally, the class has one private member, inc, returning a cyclically incremented pointer into CirQue's raw memory: 

    template<typename Data>
    Data *CirQue<Data>::inc(Data *ptr)
    {
        ++ptr;
        return ptr == d_data + d_maxSize ? d_data : ptr;
    }

22.1.5: Using CirQue objects

When objects of a class template are instantiated, only the definitions of all the template's member functions that are actually used must have been seen by the compiler.

That characteristic of templates could be refined to the point where each definition is stored in a separate function template definition file. In that case only the definitions of the function templates that are actually needed would have to be included. However, it is hardly ever done that way. Instead, the usual way to define class templates is to define the interface and to define the remaining function templates immediately below the class template's interface (defining some functions inline).

Now that the class CirQue has been defined, it can be used. To use the class its object must be instantiated for a particular data type. In the following example it is initialized for data type std::string: 

#include "cirque.h"
#include <iostream>
#include <string>
using namespace std;

int main()
{
    CirQue<string> ci(4);
    ci.push_back("1");
    ci.push_back("2");
    cout << ci.size() << ' ' << ci.front() << ' ' << ci.back() << '\n';

    ci.push_back("3");
    ci.pop_front();
    ci.push_back("4");
    ci.pop_front();
    ci.push_back("5");
    cout << ci.size() << ' ' << ci.front() << ' ' << ci.back() << '\n';

    CirQue<string> copy(ci);
    copy.pop_front();
    cout << copy.size() << ' ' << copy.front() << ' ' << copy.back() << '\n';

    int arr[] = {1, 3, 5, 7, 9};
    CirQue<int> ca(arr);
    cout << ca.size() << ' ' << ca.front() << ' ' << ca.back() << '\n';

//    int *ap = arr;
//    CirQue<int> cap(ap);
}

This program produces the following output: 

    2 1 2
    3 3 5
    2 4 5
    5 1 9

22.1.6: Default class template parameters

Different from function templates, template parameters of template classes may be given default argument values. This holds true for both template type- and template non-type parameters. If default template arguments were defined and if a class template object is instantiated without specifying arguments for its template parameters then the template parameter's defaults are used.

When defining defaults keep in mind that they should be suitable for the majority of instantiations of the class. E.g., for the class template CirQue the template's type parameter list could have been altered by specifying int as its default type: 

    template <typename Data = int>

Even though default arguments can be specified, the compiler must still be informed that object definitions refer to templates. When instantiating class template objects using default template arguments the type specifications may be omitted but the angle brackets must be retained. Assuming a default type for the CirQue class, an object of that class may be defined as: 

    CirQue<> intCirQue(10);

Default template arguments cannot be specified when defining template members. So, the definition of, e.g., the push_back member must always begin with the same template specification: 

    template <typename Data>

When a class template uses multiple template parameters, all may be given default values. Like default function arguments, once a default value is used all remaining template parameters must also use their default values. A template type specification list may not start with a comma, nor may it contain multiple consecutive commas.

22.1.7: Declaring class templates

Class templates may also be declared. This may be useful in situations where forward class declarations are required. To declare a class template, simply remove its interface (the part between the curly braces): 
    template <typename Data>
    class CirQue;
Default template arguments may also be specified when declaring class templates. However, default template arguments cannot be specified for both the declaration and the definition of a class template. As a rule of thumb default template arguments should be omitted from declarations, as class template declarations are never used when instantiating objects but are only occasionally used as forward references. Note that this differs from default parameter value specifications for member functions in ordinary classes. Such defaults are always specified when declaring the member functions in the class interface.

22.1.8: Preventing template instantiations

In C++ templates are instantiated when the address of a function template or class template object is taken or when a function template or class template is used. As described in section 22.1.7 it is possible to (forward) declare a class template to allow the definition of a pointer or reference to that template class or to allow it being used as a return type.

In other situations templates are instantiated when they are being used. If this happens many times (i.e., in many different source files) then this may slow down the compilation process considerably. Furtunately, C++ allows programmers to prevent templates from being instantiated, using the extern template syntax. Example: 

    extern template class std::vector<int>;
Having declared the class template it can be used in its translation unit. E.g., the following function properly compiles: 
#include <vector>
#include <iostream>
using namespace std;

extern template class vector<int>;

void vectorUser()
{
    vector<int> vi;
    cout << vi.size() << '\n';
}

But be careful:

22.2: Static data members

When static members are defined in class templates, they are defined for every new type for which the class template is instantiated. As they are static members, there will only be one member per type for which the class template is instantiated. For example, in a class like: 
    template <typename Type>
    class TheClass
    {
        static int s_objectCounter;
    };
There will be one TheClass<Type>::objectCounter for each different Type specification. The following object definitions result in the instantiation of just one single static variable, shared among the two objects: 
    TheClass<int> theClassOne;
    TheClass<int> theClassTwo;
Mentioning static members in interfaces does not mean these members are actually defined. They are only declared and must be defined separately. With static members of class templates this is no different. The definitions of static members are usually provided immediately following (i.e., below) the template class interface. For example, the static member s_objectCounter's definition, positioned just below its class interface, looks like this: 
    template <typename Type>                    // definition, following
    int TheClass<Type>::s_objectCounter = 0;    // the interface
Here s_objectCounter is an int and is thus independent of the template type parameter Type. Multiple instantiations of s_objectCounter for identical Types cause no problem, as the linker will remove all but one instantation from the final executable (cf. section 21.5).

In list-like constructions, where a pointer to objects of the class itself is required, the template type parameter Type must be used when defining the static variable. Example: 

    template <typename Type>
    class TheClass
    {
        static TheClass *s_objectPtr;
    };

    template <typename Type>
    TheClass<Type> *TheClass<Type>::s_objectPtr = 0;

As usual, the definition can be read from the variable name back to the beginning of the definition: s_objectPtr of the class TheClass<Type> is a pointer to an object of TheClass<Type>.

When a static variable of a template's type parameter's type is defined, it should of course not be given the initial value 0. The default constructor (e.g., Type()) is usually more appropriate. Example: 

    template <typename Type>                    // s_type's definition
    Type TheClass<Type>::s_type = Type();

22.2.1: Extended use of the keyword `typename'

Until now the keyword typename has been used to indicate a template type parameter. However, it is also used to disambiguate code inside templates. Consider the following function template: 
    template <typename Type>
    Type function(Type t)
    {
        Type::Ambiguous *ptr;

        return t + *ptr;
    }
When this code is processed by the compiler, it complains with an -at first sight puzzling- error message like: 
    4: error: 'ptr' was not declared in this scope
The error message is puzzling as it was the programmer's intention to declare a pointer to a type Ambiguous defined within the class template Type. But the compiler, confronted with Type::Ambiguous may interpret the statement in various ways. Clearly it cannot inspect Type itself trying to uncover Type's true nature as Type is a template type. Because of this Type's actual definition isn't available yet.

The compiler is confronted with two possibilities: either Type::Ambiguous is a static member of the as yet mysterious template Type, or it is a subtype of Type. As the standard specifies that the compiler must assume the former, the statement 

    Type::Ambiguous *ptr;
is interpreted as a multiplication of the static member Type::Ambiguous and the (now undeclared) entity ptr. The reason for the error message should now be clear: in this context ptr is unknown.

To disambiguate code in which an identifier refers to a subtype of a template type parameter the keyword typename must be used. Accordingly, the above code is altered into: 

    template <typename Type>
    Type function(Type t)
    {
        typename Type::Ambiguous *ptr;

        return t + *ptr;
    }
Classes fairly often define subtypes. When such subtypes appear inside template definitions as subtypes of template type parameters the typename keyword must be used to identify them as subtypes. Example: a class template Handler defines a typename Container as its template type parameter. It also defines a data member storing the iterator returned by the container's begin member. In addition Handler offers a constructor accepting any container supporting a begin member. Handler's class interface could then look like this: 
    template <typename Container>
    class Handler
    {
        Container::const_iterator d_it;

        public:
            Handler(Container const &container)
            :
                d_it(container.begin())
            {}
    };
What did we have in mind when designing this class? The final consideration is an indication that typename is required. If this is omitted and a Handler is instantiated the compiler produces a peculiar compilation error: 
    #include "handler.h"
    #include <vector>
    using namespace std;

    int main()
    {
        vector<int> vi;
        Handler<vector<int> > ph(vi);
    }
    /*
        Reported error:

    handler.h:4: error: syntax error before `;' token
    */
Clearly the line 
    Container::const_iterator d_it;
in the class Handler causes a problem. It is interpreted by the compiler as a static member instead of a subtype. The problem is solved using typename: 
    template <typename Container>
    class Handler
    {
        typename Container::const_iterator d_it;
        ...
    };
An interesting illustration that the compiler indeed assumes X::a to be a member a of the class X is provided by the error message we get when we try to compile main using the following implementation of Handler's constructor: 
    Handler(Container const &container)
    :
        d_it(container.begin())
    {
        size_t x = Container::ios_end;
    }
    /*
        Reported error:

        error: `ios_end' is not a member of type `std::vector<int,
                std::allocator<int> >'
    */

Now consider what happens if the function template introduced at the beginning of this section doesn't return a Type value, but a Type::Ambiguous value. Again, a subtype of a template type is referred to, and typename must be used: 

    template <typename Type>
    typename Type::Ambiguous function(Type t)
    {
        return t.ambiguous();
    }
Using typename in the specification of a return type is further discussed in section 23.1.1.

Typenames can be embedded in typedefs. As is often the case, this reduces the complexities of declarations and definitions appearing elsewhere. In the next example the type Iterator is defined as a subtype of the template type Container. Iterator may now be used without requiring the use of the keyword typename: 

    template <typename Container>
    class Handler
    {
        typedef typename Container::const_iterator Iterator;

        Iterator d_it;
        ...
    };

22.3: Specializing class templates for deviating types

The class CirQue can be used for many different types. Their common characteristic is that they can simply be pointed at by the class's d_data member. But this is not always as simple as it looks. What if Data turns out to be a vector<int>? For such data types the vanilla CirQue implementation cannot be used and a specialization could be considered. When considering a specialization one should also consider inheritance. Often a class derived from the class template accepting the incompatible data structure as its argument but otherwise equal to the original class template can easily be designed. The developmental advantage of inheritance over specialization is clear: the inherited class inherits the members of its base class while the specialization inherits nothing. All members defined by the original class template must be implemented again by the class template's specialization.

The specialization considered here is a true specialization in that the data members and representation used by the specialization greatly differ from the original CirQue class template. Therefore all members defined by the orginal class template must be modified to fit the specialization's data organization.

Like function template specializations class template specializations start with a template header that may or may not have an empty template parameter list. If the template parameters are directly specialized by the specialization it remains empty (e.g., CirQue's template type parameter Data is specialized for char * data). But the template parameter list may show typename Data when specializing for a vector<Data>, i.e., a vector storing any type of data. This leads to the following principle:

A template specialization is recognized by the template argument list following a function or class template's name and not by an empty template parameter list. Class template specializations may have non-empty template parameter lists. If so, a partial class template specialization is defined.

A completely specialized class has the following characteristics:

22.3.1: Example of a class specialization

Here is an example of a completely specialized CirQue class, specialized for a vector<int>. All members of the specialized class are declared, but only non-trivial implementations of its members are provided. The specialized class uses a copy of the vector passed to the constructor and implements a circular queue using its vector data member: 
#ifndef INCLUDED_CIRQUEVECTOR_H_
#define INCLUDED_CIRQUEVECTOR_H_

#include <vector>
#include "cirque.h"

template<>
class CirQue<std::vector<int>>
{
    typedef std::vector<int> IntVect;

    IntVect d_data;
    size_t d_size;

    typedef IntVect::iterator iterator;
    iterator d_front;
    iterator d_back;

    public:
        typedef int value_type;
        typedef value_type const &const_reference;

        enum Exception
        {
            EMPTY,
            FULL
        };

        CirQue();
        CirQue(IntVect const &iv);
        CirQue(CirQue<IntVect> const &other);

        CirQue &operator=(CirQue<IntVect> const &other);

        int &back();
        int &front();
        bool empty() const;
        bool full() const;
        size_t maxSize() const;
        size_t size() const;
        void pop_front();
        void push_back(int const &object);
        void swap(CirQue<IntVect> &other);

    private:
        iterator inc(iterator const &iter);
};

CirQue<std::vector<int>>::CirQue()
:
    d_size(0)
{}
CirQue<std::vector<int>>::CirQue(IntVect const &iv)
:
    d_data(iv),
    d_size(iv.size()),
    d_front(d_data.begin()),
    d_back(d_data.begin())
{}
CirQue<std::vector<int>>::CirQue(CirQue<IntVect> const &other)
:
    d_data(other.d_data),
    d_size(other.d_size),
    d_front(d_data.begin() + (other.d_front - other.d_data.begin())),
    d_back(d_data.begin() + (other.d_back - other.d_data.begin()))
{}
CirQue<std::vector<int>> &CirQue<std::vector<int>>::operator=(
                                        CirQue<IntVect> const &rhs)
{
    CirQue<IntVect> tmp(rhs);
    swap(tmp);
}
void CirQue<std::vector<int>>::swap(CirQue<IntVect> &other)
{
    char tmp[sizeof(CirQue<IntVect>)];
    memcpy(tmp, &other, sizeof(CirQue<IntVect>));
    memcpy(&other, this, sizeof(CirQue<IntVect>));
    memcpy(this, tmp, sizeof(CirQue<IntVect>));
}
void CirQue<std::vector<int>>::pop_front()
{
    if (d_size == 0)
        throw EMPTY;

    d_front = inc(d_front);
    --d_size;
}
void CirQue<std::vector<int>>::push_back(int const &object)
{
    if (d_size == d_data.size())
        throw FULL;

    *d_back = object;
    d_back = inc(d_back);
    ++d_size;
}
inline int &CirQue<std::vector<int>>::back()
{
    return d_back == d_data.begin() ? d_data.back() : d_back[-1];
}
inline int &CirQue<std::vector<int>>::front()
{
    return *d_front;
}
CirQue<std::vector<int>>::iterator CirQue<std::vector<int>>::inc(
    CirQue<std::vector<int>>::iterator const &iter)
{
    iterator tmp(iter + 1);
    tmp =  tmp == d_data.end() ? d_data.begin() : tmp;
    return tmp;
}

#endif

The next example shows how to use the specialized CirQue class: 

static int iv[] = {1, 2, 3, 4, 5};

int main()
{
    vector<int> vi(iv, iv + 5);
    CirQue<vector<int>> ci(vi);

    cout << ci.size() << ' ' << ci.front() << ' ' << ci.back() << '\n';
    ci.pop_front();
    ci.pop_front();

    CirQue<vector<int>> cp;

    cp = ci;
    cout << cp.size() << ' ' << cp.front() << ' ' << cp.back() << '\n';
    cp.push_back(6);
    cout << cp.size() << ' ' << cp.front() << ' ' << cp.back() << '\n';
}

/*
    Displays:
        5 1 5
        3 3 5
        4 3 6
*/

22.4: Partial specializations

In the previous section class template specializations were introduced. In this section we'll introduce a variant of this specialization, both in number and type of template parameters that are specialized. Partial specializations may be defined for class templates having multiple template parameters. Function templates cannot be partially specialized.

With partial specializations a subset (any subset) of template type parameters are given specific values. It is also possible to use a class template partial specialization when the intent is to specialize the class template, but to parameterize the data type that is processed by the specialization.

To start our discussion with an example of the latter use of a partial class template specialization consider the class CirQue<vector<int>> developed in the previous section. When designing CirQue<vector<int>> you may have asked yourself how many specializations you'd have to implement. One for vector<int>, one for vector<string>, one for vector<double>? As long as the data types handled by the vector used by the class CirQue<vector<...>> behaves like an int (i.e., is a value-type of class) the answer is: zero. Instead of defining full specializations for each new data type the data type itself can be parameterized, resulting in a partial specialization: 

    template <typename Data>
    class CirQue<std::vector<Data>>
    {
        ...
    };
The above class is a specialization as a template argument list is appended to the CirQue class name. But as the class template itself has a non-empty template parameter list it is in fact recognized as a partial specialization. There is one characteristic that distinguishes the implementation (subsequent to the class template's interface) of a class template member function of a partial specialization from the implementation of a member function of a full specialization. Implementations of partially specialized class template member functions receive a template header. No template headers are used when implementing fully specialized class template members.

Implementing the partial specialization for CirQue is not difficult and is left as an exercise for the reader (hints: simply change int into Data in the CirQue<vector<int>> specialization of the previous section). Remember to prefix the type iterator by typename (as in typedef typename DataVect::iterator iterator) (as discussed in section 22.2.1).

In the next subsections we'll concentrate on specializing class template non-type template parameters. These partial specializations are now illustrated using some simple concepts defined in matrix algebra, a branch of linear algebra.

22.4.1: Intermezzo: some simple matrix algebraic concepts

In this section some simple matrix algebraic terms are introduced. These terms are used in the next sections to illustrate and discuss partial specializations of class templates. Readers proficient in matrix algebra may skip this section without loss of continuity.

A matrix is commonly thought of as a table of some rows and columns, filled with numbers. Immediately we recognize an opening for using templates: the numbers might be plain double values, but they could also be complex numbers, for which our complex container (cf. section 12.5) might prove useful. Our class template is therefore provided with a DataType template type parameter. It is specified when a matrix is constructed. Some simple matrices using double values, are: 

    1   0   0           An identity matrix,
    0   1   0           (a 3 x 3 matrix).
    0   0   1

    1.2  0    0    0    A rectangular matrix,
    0.5  3.5  18  23    (a 2 x 4 matrix).

    1   2   4   8       A matrix of one row
                        (a 1 x 4 matrix), also known as a
                        `row vector' of 4 elements.
                        (column vectors are analogously defined)

Various operations are defined on matrices. They may, for example be added, subtracted or multiplied. Here we will not focus on these operations. Rather, we concentrate on some simple operations: computing marginals and sums.

Marginals are the sums of row elements or the sums of column elements of a matrix. These two kinds of marginals are also known as, respectively, row marginals and column marginals.

The following example shows a matrix, its marginals, and the sum of its values: 
    -------------------------------------
                                row
                matrix          marginals
                ---------
                1   2   3        6
                4   5   6       15
                ---------
    column      5   7   9       21  (sum)
    marginals
    -------------------------------------

22.4.2: The Matrix class template

We'll start out by introducing a class template defining a matrix. Having defined this class template we'll continue with defining several specializations.

Since matrices consist of well defined numbers of rows and columns (the dimensions of the matrix), that normally do not change when matrices are used, we might consider specifying their values as template non-type parameters. The DataType = double will be used in the majority of cases. Therefore, double can be selected as the template's default type argument. Since it's a sensible default, the DataType template type parameter is used last in the template type parameter list.

Our template class Matrix begins its life as: 

    template <size_t Rows, size_t Columns, typename DataType = double>
    class Matrix
    ...

What do we want our class template to offer?

22.4.3: The MatrixRow partial specialization

Class template partial specializations can be defined for any (subset) of template parameters. They can be defined for template type parameters and for template non-type parameters alike. Our first partial specialization defines a row of a generic Matrix, mainly (but not only) used for the construction of column marginals. Here is how such a partial specialization is designed: Now that we have defined the generic Matrix class and the partial specialization defining a single row the compiler selects the row's specialization whenever a Matrix is defined using Row = 1. For example: 
    Matrix<4, 6> matrix;        // generic Matrix template is used
    Matrix<1, 6> row;           // partial specialization is used

22.4.4: The MatrixColumn partial specialization

The partial specialization for a MatrixColumn is constructed similarly. Let's present its highlights (the full Matrix class template definition as well as all its specializations are provided in the cplusplus.yo.zip archive (at SourceForge) in the file yo/classtemplates/examples/matrix.h):

22.4.5: The 1x1 matrix: avoid ambiguity

The reader might wonder what happens if we define the following matrix: 
    Matrix<1, 1> cell;
Is this a MatrixRow or a MatrixColumn specialization? The answer is: neither.

It's ambiguous, precisely because both the columns and the rows could be used with a (different) template partial specialization. If such a Matrix is actually required, yet another specialized template must be designed.

Since this template specialization can be useful to obtain the sum of the elements of a Matrix, it's covered here as well.

Finally, the main function shown below illustrates how the Matrix class template and its partial specializations can be used: 

    #include <iostream>
    #include "matrix.h"
    using namespace std;

    int main(int argc, char **argv)
    {
        Matrix<3, 2> matrix(cin);

        Matrix<1, 2> colMargins(matrix);
        cout << "Column marginals:\n";
        cout << colMargins[0] << " " << colMargins[1] << '\n';

        Matrix<3, 1> rowMargins(matrix);
        cout << "Row marginals:\n";
        for (size_t idx = 0; idx < 3; idx++)
            cout << rowMargins[idx] << '\n';

        cout << "Sum total: " << Matrix<1, 1>(matrix) << '\n';
    }
    /*
        Generated output from input: 1 2 3 4 5 6

        Column marginals:
        9 12
        Row marginals:
        3
        7
        11
        Sum total: 21
    */

22.5: Variadic templates

Up to this point we've encountered templates defining a fixed number of template parameters. However, templates may also defined as variadic templates, allowing any number of arguments to be passed to their instantiations.

Variadic templates are defined for function templates and for class templates. Variadic templates allow us to specify an arbitrary number of template arguments of any type.

Variadic templates were added to the language to prevent us from having to define many overloaded templates and to be able to create type safe variadic functions.

Although C (and C++) support variadic functions, their use has always been deprecated in C++ as those functions are notoriously type-unsafe. Variadic function templates can be used to process objects that until now couldn't be processed properly by C-style variadic functions.

Template headers of variadic templates use the phrase typename ...Params (Params being a formal name). A variadic class template Variadic could be declared as follows: 

    template<typename ...Params> class Variadic;
Assuming the class template's definition is available then this template can be instantiated using any number of template arguments. Example: 
    class Variadic<
            int,
            std::vector<int>,
            std::map<std::string, std::vector<int>>
    > v1;
The template argument list of a variadic template can also be empty. Example: 
    class Variadic<> empty;
If this is considered undesirable using an empty template argument list can be prevented by providing one or more fixed parameters. Example: 
    template<typename First, typename ...Rest>
    class tuple;

C's function printf is a well-known example of a type-unsafe function. It is turned into a type-safe function when it is implemented as a variadic function template. Not only does this turn the function into a type-safe function but it is also automatically extended to accept any type that can be defined by C++. Here is a possible declaration of a variadic function template printcpp: 

    template<typename ...Params>
    void printcpp(std::string const &strFormat, Params ...parameters);
The ellipsis (...) used in the declaration serves two purposes: C++ offers no syntax to access the individual template arguments directly. However, the arguments can be visited recursively. An example is provided in the next section. The number of arguments is determined using a new invocation of the sizeof operator: 
    template<typename ...Params>
    struct StructName
    {
        enum: size_t { s_size = sizeof ...(Params) };
    };

    // StructName<int, char>::s_size          -- initialized to 2

22.5.1: Defining and using variadic templates

The arguments associated with a variadic template parameter are not directly available to the implementation of a function or class template. We have to resort to other means to obtain them.

By defining a partial specialization of a variadic template, explicitly defining an additional template type parameter, we can associate the first template argument of a parameter pack with this additional (first) type parameter. The setup of such a variadic function template (e.g., printcpp, see the previous section) is as follows:

The overloaded non-template function prints the remainder of the format string, en passant checking for any left-over format specifications: 

    void printcpp(string const &format)
    {
        size_t left = 0;
        size_t right = 0;

        while (true)
        {
            if ((right = format.find('%', right)) == string::npos)
                break;
            if (format.find("%%", right) != right)
                throw std::runtime_error(
                            "printcpp: missing arguments");
            ++right;
            cout << format.substr(left, right - left);
            left = ++right;
        }
        cout << format.substr(left);
    }

Here is the variadic function template's implementation: 

    template<typename First, typename ...Params>
    void printcpp(std::string const &format, First value, Params ...params)
    {
        size_t left = 0;
        size_t right = 0;
        while (true)
        {
            if ((right = format.find('%', right)) == string::npos)      // 1
                throw std::runtime_error("printcpp: too many arguments");

            if (format.find("%%", right) != right)                      // 2
                break;

            ++right;
            cout << format.substr(left, right - left);
            left = ++right;
        }
        cout << format.substr(left, right - left) << value;
        printcpp(format.substr(right + 1), params...);
   }
Make sure that the overloaded function is at least declared before the compiler processes the function template's definition or it won't call the overloaded function printcpp when compiling the function template.

Different from C's printf function printcpp only recognizes % and %% as format specifiers. The above implementation does not recognize, e.g., field widths. Type specifiers like %c and %x are of course not needed as ostream's insertion operator is aware of the types of the arguments that are inserted into the ostream. Extending the format specifiers so that field widths etc. are recognized by this printcpp implementation is left as an exercise to the reader. Here is an example showing how printcpp can be called: 

    printcpp("Hello % with %%main%% called with % args"
                                            " and a string showing %\n",
        "world", argc, string("A String"));

22.5.2: Perfect forwarding

Consider string's member insert. String::insert has several overloaded implementations. It can be used to insert text (completely or partially) provided by a string or by a char const * argument; to insert single characters a specified number of times; iterators can be used to specify the range of characters to be inserted; etc., etc.. All in all, string offers as many as five overloaded insert members.

Assume the existence of a class Inserter that is used to insert information into all kinds of objects. Such a class could have a string data member into which information can be inserted. Inserter's interface only partially has to copy string's interface to realize this: only string::insert's interfaces must be duplicated. The members duplicating interfaces often contain one statement (calling the appropriate member function of the object's data member) and are for this reason often implemented in-line. Such wrapper functions merely forward their parameters to the matching member functions of the object's data member.

Another example is found in factory functions that also frequently forward their parameters to the constructors of objects that they return.

C++ simplifies and generalizes forwarding of parameters by offering perfect forwarding, implemented through rvalue references and variadic templates. With perfect forwarding the arguments passed to functions are `perfectly forwarded' to nested functions. Forwarding is called perfect as the arguments are forwarded in a type-safe way. To use perfect forwarding nested functions must define parameter lists matching the forwarding parameters both in types and number.

Perfect forwarding is easily implemented:

In the next example perfect forwarding is used to implement one member Inserter::insert that can be used to call any of the five overloaded string::insert members. The insert function that's actually called now simply depends on the types and number of arguments that are passed to Inserter::insert: 

    class Inserter
    {
        std::string d_str;  // somehow initialized
        public:
                            // constructors not implemented,
                            // but see below
            Inserter();
            Inserter(std::string const &str);
            Inserter(Inserter const &other);
            Inserter(Inserter &&other);

            template<typename ...Params>
            void insert(Params &&...params)
            {
                d_str.insert(std::forward<Params>(params)...);
            }
    };

A factory function returning an Inserter can also easily be implemented using perfect forwarding. Rather than defining four overloaded factory functions a single one now suffices. By providing the factory function with an additional template type parameter specifying the class of the object to construct the factory function is turned into a completely general factory function: 

    template <typename Class, typename ...Params>
    Class factory(Params &&...params)
    {
        return Class(std::forward<Params>(params)...);
    }
Here are some examples showing its use: 
    Inserter inserter(factory<Inserter>("hello"));
    string delimiter(factory<string>(10, '='));
    Inserter copy(factory<Inserter>(inserter));

The function std::forward is provided by the standard library. It performs no magic, but merely returns params as a nameless object. That way it acts like std::move that also removes the name from an object, returning it as a nameless object. The unpack operator has nothing to do with the use of forward but merely tells the compiler to apply forward to each of the arguments in turn. Thus it behaves similarly to C's ellipsis operator used by variadic functions.

Perfect forwarding was introduced in section 21.4.5: a template function defining a Type &&param, with Type being a template type parameter converts Type && to Tp & if the function is called with an argument of type Tp &. Otherwise it binds Type to Tp, with param being defined as Tp &&param. As a result an lvalue argument binds to an lvalue-type (Tp &), while an rvalue argument binds to an rvalue-type (Tp &&).

The function std::forward merely passes the argument (and its type) on to the called function or object. Here is its simplified implementation: 

    typedef <type T>
    T &&forward(T &&a)
    {
        return a;
    }
Since T && turns into an lvalue reference when forward is called with an lvalue (or lvalue reference) and remains an rvalue reference if forward is called with an rvalue reference, and since forward (like std::move) anonymizes the variable passed as argument to forward, the argument value is forwarded while passing its type from the function's parameter to the called function's argument.

This is called perfect forwarding as the nested function can only be called if the types of the arguments that were used when calling the `outer' function (e.g., factory) exactly match the types of the parameters of the nested function (e.g., Class's constructor). Perfect forwarding therefore is a tool to realize type safety.

A cosmetic improvement to forward requires users of forward to specify the type to use rather than to have the compiler deduct the type as a result of the function template parameter type deduction's process. This is realized by a small support struct template: 

    template <typename T>
    struct identity
    {
        typedef T type;
    };
This struct merely defines identity::type as T, but as it is a struct it must be specified explicitly. It cannot be determined from the function's argument itself. The subtle modification to the above implementation of forward thus becomes (cf. section 22.2.1 for an explanation of the use of typename): 
    typedef <type T>
    T &&forward(typename identity<T>::type &&arg)
    {
        return arg;
    }
Now forward must explicitly state arg's type, as in: 
    std::forward<Params>(params)

Using the std::forward function and the rvalue reference specification is not restricted to the context of parameter packs. Because of the special way rvalue references to template type parameters are treated (cf. section 21.4.5) they can profitably be used to forward individual function parameters as well. Here is an example showing how an argument to a function can be forwarded from a template to a function that is itself passed to the template as a pointer to an (unspecified) function: 

    template<typename Fun, typename ArgType>
    void caller(Fun fun, ArgType &&arg)
    {
        fun(std::forward<ArgType>(arg));
    }
A function display(ostream &out) and increment(int &x) may now both be called through caller. Example: 
    caller(display, cout);
    int x = 0;
    caller(increment, x);

22.5.3: The unpack operator

The unpack operator is used to obtain template arguments in many situations. No mechanism other than recursion (as shown in section 22.5.1) is available to obtain the individual types and values of a variadic template.

The unpack operator can also be used to define template classes that are derived from any number of base classes. Here is how it's done: 

    template <typename ...BaseClasses>
    class Combi: public BaseClasses...          // derive from base classes
    {
        public:
                                                // specify base class objects
                                                // to its constructor using
                                                // perfect forwarding
            Combi(BaseClasses &&...baseClasses)
            :
                BaseClasses(baseClasses)...     // use base class initializers
            {}                                  // for each of the base
    };                                          // classes
This allows us to define classes that combine the features of any number of other classes. If the class Combi is derived of classes A, B, and C then Combi is-an A, B, and C. It should of course be given a virtual destructor. A Combi object can be passed to functions expecting pointers or references to any of its base class type objects. Here is an example defining Combi as a class derived from a vector of complex numbers, a string and a pair of ints and doubles (using uniform intializers in a sequence matching the sequence of the types specified for the used Combi type): 
    typedef Combi<
        vector<complex<double>>, string, pair<int, double>
    > MultiTypes;

    MultiTypes mt = {{3.5, 4}, "mt", {1950, 1.72}};

The same construction can also be used to define template data members supporting variadic type lists such as tuples (cf. section 22.6). Such a class could be designed along these lines: 

    template <typename ...Types>
    struct Multi
    {
        std::tuple<Types...> d_tup;        // define tuple for Types types

        Multi(Types ...types)
        :                                   // initialize d_tup from Multi's
            d_tup(std::forward<Types>(types)...)   //             arguments
        {}
    };

The ellipses that are used when forwarding parameter packs are essential. The compiler considers their omission an error. In the following struct definition it was the intent of the programmer to pass a parameter pack on to a nested object construction but ellipses were omitted while specifying the template parameters, resulting in a parameter packs not expanded with `...' error message: 

    template <int size, typename ...List>
    struct Call
    {
        Call(List &&...list)
        {
            Call<size - 1, List &&> call(std::forward<List>(list)...);
        }
    };
Instead of the above definition of the call object the programmer should have used: 
    Call<size - 1, List &&...> call(std::forward<List>(list)...);

22.5.4: Non-type variadic templates

Variadic templates not necesssarily define template types. Non-types can also be used with variadic templates. The following function template accepts any series of int values, forwarding these values to a class template. The class template defines an enum value result which is returned by the function, unless no int values were specified, in which case 0 is returned. 
    template <int ... Ints>
    int forwarder()
    {
        return computer<Ints ...>::result;  // forwarding the Ints
    }

    template <>     // specialization if no ints are provided
    int forwarder<>()
    {
        return 0;
    }

    // use as:
    cout << forwarder<1, 2, 3>() << ' ' << forwarder<>() << '\n';
The sizeof operator can be used for variadic non-type parameters as well: sizeof...(Ints) would return 3 when used in the first function template for forwarder<1, 2, 3>().

Variadic non-type parameters are used to define variadic literal operators, introduced in section 23.3.

22.5.5: A bare bones `not_fn' negator

Section 18.1.4.2 covered the not1 and not2 negators. These negators cannot always be used in combination with the bind function template, and there use is limited to situations where one or two arguments are used. It is likely that in the upcoming C++17 standard they will either be deprecated or they will be augmented with a more generic negator, for which the name not_fn has been coined.

In this section we'll have a look at a possible bare bones implementation of such a not_fn negator.

Let's first have a look at how not_fn can be used. When discussing the negators it was noted that the second of the following two statements won't compile: 

    count_if(vs.begin(), vs.end(), 
        bind(not2(greater_equal<string>()), _1, reftext));

    count_if(vs.begin(), vs.end(),
        not1(bind(greater_equal<string>()), _1, reftext));
Here we'll develop an alternative, not_fn, replacing not1 and not2 in the above statements: 
    count_if(vs.begin(), vs.end(),                          // 1
        bind(not_fn(greater_equal<string>()), _1, reftext));

    count_if(vs.begin(), vs.end(),                          // 2
        not_fn(bind(greater_equal<string>()), _1, reftext));
In statement 1 not_fn is passed the greater_equal<string>() functor, in statement 2 not_fn is passed a functor, returned by bind. By defining not_fn as a template function the compiler is able to determine the argument's type. Thus not_fn merely needs a typename Fun template type parameter.

When used, not_fn's function call operators may receive different types and numbers of arguments (in statement 1 it receives two arguments from bind's function call operator, in statement 2 it receives one argument from count_if). Those arguments must in turn be forwarded to the function call operator of the function object that was passed to not_fn. Summarizing we have this situation (see figure 25):

  1. Some function or functor must be called, e.g., greater_equal, but its return value must be negated;
  2. The function is passed to the function template not_fn. The compiler determines its type. This type is used to construct a not_fn_ class template, which is returned by not_fn;
  3. The not_fn_ object itself is a functor, and its operator() member perfectly forwards its arguments to the function originally specified a steps 1 and 2, and returns the negated return value of the original function;
  4. Some calling function receives the not_fn_ object, and calls its operator() with the appropriate argument(s).

Figure 25 is shown here.
Figure 25: Using not_fn

In step 2 not_fn is used. It is defined like this: 

    template <typename Fun>
    not_fn_<Fun> not_fn(Fun const &fun)
    {
        return not_fn_<Fun>(fun);
    }
This function returns a not_fn_ function object, initialized with the functor to call (e.g., greater_equal<string>() or the functor returned by bind).

Also in step 2 not_fn_'s constructor is mentioned, saving a reference to the function mentioned in step 1: 

    template <typename Fun>
    struct not_fn_
    {
        Fun const &d_fun;
    
        not_fn_(Fun const &fun)
        :
            d_fun(fun)
        {}
        ...
    };

In step 3 not_fn_'s function call operator is used. It perfectly forwards its arguments to step 1's function, which can be accessed via its d_fun data member. The function call operator returns d_fun's negated return value: 

    template <typename ... ParTypes>
    bool operator()(ParTypes && ...types)
    {
        return not d_fun(std::forward<ParTypes>(types)...);
    }

The next example shows how not_fn can be used: using equal_to<string>() two ways to count the number of elements in a string vector that are not equal to "b" are shown. The program's output displays two twos: 

     1: int main()
     2: {
     3:     vector<string> vs {"a", "a", "b"};
     4:     string reftext {"b"};
     5:
     6:     cout <<
     7:         count_if(vs.begin(), vs.end(),
     8:             bind(not_fn(equal_to<string>()), _1, reftext)) << '\n' <<
     9:         count_if(vs.begin(), vs.end(),
    10:             not_fn(bind(equal_to<string>(), _1, reftext))) << '\n';
    11: }

22.6: Tuples

C++ offers a generalized pair container: the tuple, covered in this section. Before tuples can be used the header file <tuple> must be included.

Whereas std::pair containers have limited functionality and only support two members, tuples have slightly more functionality and may contain an unlimited number of different data types. In that respect a tuple can be considered the `template's answer to C's struct'.

A tuple's generic declaration (and definition) uses the variadic template notation: 

    template <class ...Types>
    class tuple;
Here is an example of its use: 
    typedef std::tuple<int, double &, std::string, char const *> tuple_idsc;

    double pi = 3.14;
    tuple_idsc idsc(59, pi, "hello", "fixed");

    // access a field:
    std::get<2>(idsc) = "hello world";
The std::get<idx>(tupleObject) function template returns a reference to the idxth (zero based) field of the tuple tupleObject. The index is specified as the function template's non-type template argument.

The C++14 standard also supports type-based tuple addressing. It can be used for tuple types used once in a tuple definition (if the same type is used repeatedly referring to that type introduces an ambiguity). The next example shows how to refer to the elements in the above example by type: 

    get<int>(idsc)              // 59
    get<double &>(idsc)         // 3.14
    get<string>(idsc)           // "hello"s
    get<char const *>(idsc)     // "fixed"

Tuples may be constructed without specifying initial values. Primitive types are initialized to zeroes; class type fields are initialized by their default constructors. Be aware that in some situations the construction of a tuple may succeed but its use may fail. Consider: 

    tuple<int &> empty;
    cout << get<0>(empty);
Here the tuple empty cannot be used as its int & field is an undefined reference. However, empty's construction succeeds.

Tuples may be assigned to each other if their type lists are identical; if supported by their constituent types copy constructors are available as well. Copy construction and assignment is also available if a right-hand type can be converted to its matching left-hand type or if the left-hand type can be constructed from the matching right-hand type. Tuples (matching in number and (convertible) types) can be compared using relational operators as long as their constituent types support comparisons. In this respect tuples are like pairs.

Tuples offer the following static elements (using compile-time initialization):

The unpack operator can also be used to forward the arguments of a constructor to a tuple data member. Consider a class Wrapper that is defined as a variadic template: 

    template <typename ...Params>
    class Wrapper
    {
        ...
        public:
            Wrapper(Params &&...params);
    };
This class may be given a tuple data member which should be initialized by the types and values that are used when initializing an object of the class Wrapper using perfect forwarding. Comparable to the way a class may inherit from its template types (cf. section 22.5.3) it may forward its types and constructor arguments to its tuple data member: 
    template <typename ...Params>
    class Wrapper
    {
        std::tuple<Params...> d_tuple;     // same types as used for
                                            // Wrapper itself
        public:
            Wrapper(Params &&...params)
            :                               // initialize d_tuple with
                                            // Wrapper's arguments
                d_tuple(std::forward<Params>(params)...)
            {}
    };

22.7: Computing the return type of function objects

As amply illustrated in chapter 19 function objects play an important role with generic algorithms. Like generic algorithms themselves, function objects can be generically defined as members of class templates. If the function call operators (operator()) of such classes define parameters then the types of those parameters may also be abstracted by defining the function call operators themselves as member templates. Example: 
    template <typename Class>
    class Filter
    {
        Class obj;
        public:
            template <typename Param>
            Param operator()(Param const &param) const
            {
                return obj(param);
            }
    };
The template class Filter is a wrapper around Class, filtering Class's function call operator through its own function call operator. In the above example the return value of Class's function call operator is simply passed on, but any other manipulation is of course also possible.

A type that is specified as Filter's template type argument may of course have multiple function call operators: 

    struct Math
    {
        int operator()(int x);
        double operator()(double x);
    };
Math objects can now be filtered using Filter<Math> fm using Math's first or second function call operator, depending on the actual argument type. With fm(5) the int-version is used, with fm(12.5) the double-version is used.

However, this scheme doesn't work if the function call operators have different return and argument types. Because of this the following class Convert cannot be used with Filter: 

    struct Convert
    {
        double operator()(int x);           // int-to-double
        std::string operator()(double x);   // double-to-string
    };
This problem can be tackled successfully by the class template std::result_of<Functor(Typelist)>. Before using std::result_of the header file <functional> must be included.

The result_of class template offers a typedef (type), representing the type that is returned by Functor<TypeList>. It can be used as follows to improve the implementation of Filter: 

    template <typename Class>
    class Filter
    {
        Class obj;
        public:
            template <typename Arg>
                typename std::result_of<Class(Arg)>::type
                operator()(Arg const &arg) const
                {
                    return obj(arg);
                }
    };
Using this definition, Filter<Convert> fc can be constructed. Now fc(5) returns a double, while fc(4.5) returns a std::string.

The class Convert must define the relationships between its function call operators and their return types. Predefined function objects (like those in the standard template library) already do so, but self-defined function objects must do this explicitly.

If a function object class defines only one function call operator it can define its return type by a typedef. If the above class Convert would only define the first of its two function call operators then the typedef (in the class's public section) should be: 

    typedef double type;

If multiple function call operators are defined, each with its own signature and return type, then the association between signature and return type is set up as follows (all in the class's public section):

22.8: Instantiating class templates

Class templates are instantiated when an object of a class template is defined. When a class template object is defined or declared its template parameters must explicitly be specified.

Template parameters are also specified when default template parameter values are specified albeit that in that case the compiler provides the defaults (cf. section 22.4 where double is used as the default type to use for the template's DataType parameter). The actual values or types of template parameters are never deduced from arguments as is done with function template parameters. So to define a Matrix of complex-valued elements, the following syntax is used: 

    Matrix<3, 5, std::complex> complexMatrix;
Since the class template Matrix uses a default data type a matrix of double-valued elements can be defined like this: 
    Matrix<3, 5> doubleMatrix;
A class template object may be declared using the keyword extern. For example, to declare the matrix complexMatrix use: 
    extern Matrix<3, 5, std::complex> complexMatrix;
A class template declaration suffices to compile return values or parameters that are of class template types. Example: the following source file may be compiled, although the compiler hasn't seen the definition of the Matrix class template. Generic classes and (partial) specializations may all be declared. A function expecting or returning a class template object, reference, or parameter automatically becomes a function template itself. This is necessary to allow the compiler to tailor the function to the types of various actual arguments that may be passed to the function: 
    #include <cstddef>

    template <size_t Rows, size_t Columns, typename DataType = double>
    class Matrix;

    template <size_t Columns, typename DataType>
    class Matrix<1, Columns, DataType>;

    Matrix<1, 12> *function(Matrix<2, 18, size_t> &mat);

When class templates are used the compiler must first have seen their implementations. So, template member functions must be known to the compiler when the template is instantiated. This does not mean that all members of a template class are instantiated or must have been seen when a class template object is defined. The compiler only instantiates those members that are actually used. This is illustrated by the following simple class Demo that has two constructors and two members. When we use one constructor and call one member in main note the sizes of the resulting object file and executable program. Next the class definition is modified in that the unused constructor and member are commented out. Again we compile and link the program. Now observe that these latter sizes are identical to the former sizes. There are other ways to illustrate that only used members are instantiated. The nm program could be used. It shows the symbolic contents of object files. Using nm we'll reach the same conclusion: only template member functions that are actually used are instantiated. Here is the class template Demo that was used for our little experiment. In main only the first constructor and the first member function are called and thus only these members were instantiated: 

    #include <iostream>

    template <typename Type>
    class Demo
    {
        Type d_data;
        public:
            Demo();
            Demo(Type const &value);
            void member1();
            void member2(Type const &value);
    };
    template <typename Type>
    Demo<Type>::Demo()
    :
        d_data(Type())
    {}
    template <typename Type>
    void Demo<Type>::member1()
    {
        d_data += d_data;
    }

    // the following members should be commented out before
    // compiling for the 2nd time:

    template <typename Type>
    Demo<Type>::Demo(Type const &value)
    :
        d_data(value)
    {}
    template <typename Type>
    void Demo<Type>::member2(Type const &value)
    {
        d_data += value;
    }

    int main()
    {
        Demo<int> demo;
        demo.member1();
    }

22.9: Processing class templates and instantiations

In section 21.13 the distinction between code depending on template parameters and code not depending on template parameters was introduced. The same distinction also holds true when class templates are defined and used.

Code not depending on template parameters is verified by the compiler when the template is defined. If a member function in a class template uses a qsort function, then qsort does not depend on a template parameter. Consequently, qsort must be known to the compiler when it encounters qsort's function call. In practice this implies that the <cstdlib> header file must have been read by the compiler before it is able to compile the class template definition.

On the other hand, if a template defines a <typename Ret> template type parameter to parameterize the return type of some template member function as in: 

    Ret member();
then the compiler may encounter member or the class to which member belongs in the following locations:

22.10: Declaring friends

Friend functions are normally constructed as support (free) functions of a class that cannot be implemented and declared as class members. The insertion operator for output streams is a well known example. Friend classes are most often seen in the context of nested classes. Here the inner class declares the outer class as its friend (or the other way around). Again we see a support mechanism: the inner class is constructed to support the outer class.

Like ordinary classes, class templates may declare other functions and classes as their friends. Conversely, ordinary classes may declare template classes as their friends. Here too, the friend is constructed as a special function or class augmenting or supporting the functionality of the declaring class. Although the friend keyword can be used by any type of class (ordinary or template) when using class templates the following cases should be distinguished:

22.10.1: Non-templates used as friends in templates

A class template may declare an ordinary function, ordinary member function or ordinary class as its friend. Such a friend may access the class template's private members.

Concrete classes and ordinary functions can be declared as friends, but before a single member function of a class can be declared as a friend, the compiler must have seen the class interface declaring that member. Let's consider the various possibilities:

22.10.2: Templates instantiated for specific types as friends

With bound friend class or function templates there is a one-to-one mapping between the template arguments of the friend templates and the template arguments of the class templates declaring them as friends. In this case, the friends themselves are templates too. Here are the various possibilities:

Finally, the following example can be used as a prototype for situations where bound friends are useful: 

    template <typename T>   // a function template
    void fun(T *t)
    {
        t->not_public();
    };
    template<typename X>    // a free member function template
    bool operator==(A<X> const &lhs, A<X> const &rhs);
    template <typename X>   // a class template
    class A
    {                       // fun() is used as friend bound to A,
                            // instantiated for X, whatever X may be
        friend void fun<A<X>>(A<X> *);
                            // operator== is a friend for A<X> only
        friend  bool operator==<>(A<X> const &lhs, A<X> const &rhs);

        int d_data = 10;

        public:
            A();

        private:
            void not_public();
    };
    template <typename X>
    A<X>::A()
    {
        fun(this);
    }
    template <typename X>
    void A<X>::not_public()
    {}
    template<typename X>    // may access lhs/rhs's private data
    bool operator==(A<X> const &lhs, A<X> const &rhs)
    {
        return lhs.d_data == rhs.d_data;
    }

    int main()
    {
        A<int> a;

        fun(&a);            // fun instantiated for A<int>.
    }

22.10.3: Unbound templates as friends

When a friend is declared as an unbound friend it merely declares an existing template to be its friend (no matter how it is instantiated). This may be useful in situations where the friend should be able to instantiate objects of class templates declaring the friend, allowing the friend to access the instantiated object's private members. Functions, classes, and member functions may all be declared as unbound friends.

Here are the syntactic conventions declaring unbound friends:

22.10.4: Extended friend declarations

Through extended friend declarations, which are also available for class templates, template type parameters can be declared as friends. A template type argument, however, does not necessarily have to be a type for which the keyword friend makes sense, like int. In those cases the friend declaration is simply ignored.

Consider the following class template, declaring Friend as a friend: 

    template <typename Friend>
    class Class
    {
        friend Friend;
        void msg();             // private, displays some message
    };
Now, an actual Friend class may access all of Class's members 
    class Concrete
    {
        Class<Concrete> d_class;
        Class<std::string> d_string;

       public:
            void msg()
            {
                d_class.msg();    // OK: calls private Class<Concrete>::msg()
                //d_string.msg(); // fails to compile: msg() is private
            }
    };
A declaration like Class<int> intClass is also OK, but here the friend declaration is simply ignored. After all, there are no `int members' to access Class<int>'s private members.

22.11: Class template derivation

Class templates can be used for inheritance purposes as well. When a class template is used in class derivation, the following situations should be distinguished: These three variants of class template derivation are elaborated in this and the upcoming sections.

Consider the following base class: 

    template<typename T>
    class Base
    {
        T const &t;

        public:
            Base(T const &t);
    };
The above class is a class template that can be used as a base class for the following derived class template Derived: 
    template<typename T>
    class Derived: public Base<T>
    {
        public:
            Derived(T const &t);
    };
    template<typename T>
    Derived<T>::Derived(T const &t)
    :
        Base(t)
    {}
Other combinations are also possible. The base class may be instantiated by specifying template arguments, turning the derived class into an ordinary class (showing a class object's definition as well): 
    class Ordinary: public Base<int>
    {
        public:
            Ordinary(int x);
    };
    inline Ordinary::Ordinary(int x)
    :
        Base(x)
    {}

    Ordinary ordinary(5);
This approach allows us to add functionality to a class template, without the need for constructing a derived class template.

Class template derivation pretty much follows the same rules as ordinary class derivation, not involving class templates. Some subtleties that are specific for class template derivation may easily cause confusion like the use of this when members of a template base class are called from a derived class. The reasons for using this are discussed in section 23.1. In the upcoming sections the focus will be on the class derivation proper.

22.11.1: Deriving ordinary classes from class templates

When an existing class template is used as a base class for deriving an ordinary class, the class template parameters are specified when defining the derived class's interface. If in a certain context an existing class template lacks a particular functionality, then it may be useful to derive an ordinary class from a class template. For example, although the class map can easily be used in combination with the find_if() generic algorithm (section 19.1.16), it requires the construction of a class and at least two additional function objects of that class. If this is considered too much overhead then extending a class template with tailor-made functionality might be considered.

Example: a program executing commands entered at the keyboard might accept all unique initial abbreviations of the commands it defines. E.g., the command list might be entered as l, li, lis or list. By deriving a class Handler from 

    map<string, void (Handler::*)(string const &cmd)>
and by defining a member function process(string const &cmd) to do the actual command processing a program might simply execute the following main() function: 
    int main()
    {
        string line;
        Handler cmd;

        while (getline(cin, line))
            cmd.process(line);
    }

The class Handler itself is derived from a std::map, in which the map's values are pointers to Handler's member functions, expecting the command line entered by the user. Here are Handler's characteristics:

22.11.2: Deriving class templates from class templates

Although it's perfectly acceptable to derive an ordinary class from a class template, the resulting class of course has limited generality compared to its template base class. If generality is important, it's probably a better idea to derive a class template from a class template. This allows us to extend an existing class template with new functionality or to override the functionality of the existing class template.

The class template SortVector presented below is derived from the existing class template std::vector. It allows us to perform a hierarchic sort of its elements using any ordering of any data members its data elements may contain. To accomplish this there is but one requirement. SortVector's data type must offer dedicated member functions comparing its members.

For example, if SortVector's data type is an object of class MultiData, then MultiData should implement member functions having the following prototypes for each of its data members which can be compared: 

    bool (MultiData::*)(MultiData const &rhv)
So, if MultiData has two data members, int d_value and std::string d_text and both may be used by a hierarchic sort, then MultiData should offer the following two members: 
    bool intCmp(MultiData const &rhv);  // returns d_value < rhv.d_value
    bool textCmp(MultiData const &rhv); // returns d_text  < rhv.d_text
Furthermore, as a convenience it is assumed that operator<< and operator>> have been defined for MultiData objects.

The class template SortVector is directly derived from the template class std::vector. Our implementation inherits all members from that base class. It also offers two simple constructors: 

    template <typename Type>
    class SortVector: public std::vector<Type>
    {
        public:
            SortVector()
            {}
            SortVector(Type const *begin, Type const *end)
            :
                std::vector<Type>(begin, end)
            {}

Its member hierarchicSort is the true raison d'être for the class. It defines the hierarchic sort criteria. It expects a pointer to a series of pointers to member functions of the class Type as well as a size_t representing the size of the array.

The array's first element indicates Type's most significant sort criterion, the array's last element indicates the class's least significant sort criterion. Since the stable_sort generic algorithm was designed explicitly to support hierarchic sorting, the member uses this generic algorithm to sort SortVector's elements. With hierarchic sorting, the least significant criterion should be sorted first. hierarchicSort's implementation is therefore easy. It requires a support class SortWith whose objects are initialized by the addresses of the member functions passed to the hierarchicSort() member: 

    template <typename Type>
    void SortVector<Type>::hierarchicSort(
                bool (Type::**arr)(Type const &rhv) const,
                size_t n)
    {
        while (n--)
            stable_sort(this->begin(), this->end(), SortWith<Type>(arr[n]));
    }

The class SortWith is a simple wrapper class around a pointer to a predicate function. Since it depends on SortVector's actual data type the class SortWith must also be a class template: 

    template <typename Type>
    class SortWith
    {
       bool (Type::*d_ptr)(Type const &rhv) const;

SortWith's constructor receives a pointer to a predicate function and initializes the class's d_ptr data member: 

    template <typename Type>
    SortWith<Type>::SortWith(bool (Type::*ptr)(Type const &rhv) const)
    :
        d_ptr(ptr)
    {}

Its binary predicate member (operator()) must return true if its first argument should eventually be placed ahead of its second argument: 

    template <typename Type>
    bool SortWith<Type>::operator()(Type const &lhv, Type const &rhv) const
    {
        return (lhv.*d_ptr)(rhv);
    }

The following examples, which can be embedded in a main function, provides an illustration:

After compiling the program the following command can be given: 
    echo a 1 b 2 a 2 b 1 | a.out
This results in the following output: 
    a 1 b 2 a 2 b 1
    ====
    a 1 a 2 b 1 b 2
    ====
    a 1 b 1 a 2 b 2
    ====

22.11.3: Deriving class templates from ordinary classes

An ordinary class may be used as the base class for deriving a template class. The advantage of such an inheritance tree is that the base class's members may all be compiled beforehand. When objects of the class template are now instantiated only the actually used members of the derived class template must be instantiated.

This approach may be used for all class templates having member functions whose implementations do not depend on template parameters. These members may be defined in a separate class which is then used as a base class of the class template derived from it.

As an illustration of this approach we'll develop such a class template below. We'll develop a class Table derived from an ordinary class TableType. The class Table displays elements of some type in a table having a configurable number of columns. The elements are either displayed horizontally (the first k elements occupy the first row) or vertically (the first r elements occupy a first column).

When displaying the table's elements they are inserted into a stream. The table is handled by a separate class (TableType), implementing the table's presentation. Since the table's elements are inserted into a stream, the conversion to text (or string) is implemented in Table, but the handling of the strings themselves is left to TableType. We'll cover some characteristics of TableType shortly, concentrating on Table's interface first:

This completes the implementation of the class Table. Note that this class template only has three members, two of them being constructors. Therefore, in most cases only two function templates must be instantiated: a constructor and the class's fill member. For example, the following defines a table having four columns, vertically filled by strings extracted from the standard input stream: 

    Table<istream_iterator<string> >
        table(istream_iterator<string>(cin), istream_iterator<string>(),
              4, TableType::VERTICAL);
The fill-direction is specified as TableType::VERTICAL. It could also have been specified using Table, but since Table is a class template its specification would have been slightly more complex: Table<istream_iterator<string> >::VERTICAL.

Now that the Table derived class has been designed, let's turn our attention to the class TableType. Here are its essential characteristics:

The support class TableSupport is used to display headers, footers, captions and separators. It has four virtual members to perform those tasks (and, of course, a virtual constructor):

The reader is referrred to the cplusplus.yo.zip archive for the full implementation of the classes Table, TableType and TableSupport. Here is a little program showing their use: 
    /*
                                  table.cc
    */

    #include <fstream>
    #include <iostream>
    #include <string>
    #include <iterator>
    #include <sstream>

    #include "tablesupport/tablesupport.h"
    #include "table/table.h"

    using namespace std;
    using namespace FBB;

    int main(int argc, char **argv)
    {
        size_t nCols = 5;
        if (argc > 1)
        {
            istringstream iss(argv[1]);
            iss >> nCols;
        }

        istream_iterator<string>   iter(cin);   // first iterator isn't const

        Table<istream_iterator<string> >
            table(iter, istream_iterator<string>(), nCols,
                  argc == 2 ? TableType::VERTICAL : TableType::HORIZONTAL);

        cout << table << '\n';
    }
    /*
        Example of generated output:
        After: echo a b c d e f g h i j | demo 3
            a e i
            b f j
            c g
            d h
        After: echo a b c d e f g h i j | demo 3 h
            a b c
            d e f
            g h i
            j
    */

22.12: Static Polymorphism

Chapter 14 introduced polymorphism. Polymorphism allows us to use a base class's interface to call implementations which are defined in derived classes. Traditionally this involves defining Vtables for polymorphic classes, containing pointers to functions that can be overridden in derived classes. Objects of polymorphic classes feature hidden pointers, pointing to their class's Vtables. This type of polymorphism is called dynamic polymorphism, involving late binding as the function to call is determined run-time, rather than compile-time.

In many programs, however, using dynamic polymorphism isn't really required. Usually the derived class objects that are passed to functions expecting base class references are invariants: at fixed locations in programs fixed class types are used to create objects. The polymorphic nature of these objects is used inside the functions that receive these objects, expecting references to their base classes.

The disadvantages of this scheme are that, firstly, inside the functions expecting references to polymorphic base classes execution is somewhat slowed down precisely because of late-binding. Member functions aren't directly called, but are called indirectly via the object's vpointer and their derived class's Vtable. Secondly, programs using dynamic polymorphism tend to become somewhat bloated compared to programs using static binding. The code bloat is caused by the requirement to satisfy at link-time all the references that are mentioned in all the object files comprising the final program. This requirement forces the linker to link all the functions whose addresses are stored in the Vtables of all polymorphic classes, even if these functions are never actually called.

Static polymorphism allows us to avoid these disadvantages. It can be used instead of dynamic polymorphism in cases where the abovementioned invariant holds. Static polymorphism, also called the curiously recurring template pattern, is an example of template meta programming (see also chapter 23 for additional examples of template meta programming).

Whereas dynamic polymorphism is based on the concepts of vpointers, Vtables, and function overriding, static polymorphism capitalizes on the fact that function templates (c.q., member templates) are only compiled into executable code when they are actually called. This allows us to write code calling functions which are completely non-existent when we write our code. This phenomenon shouldn't worry us too much. After all, we use a comparable approach when calling a purely virtual function of an abstract base class. The function is really called, but which function will actually be called is determined later in time. With dynamic polymorphism it is determined run-time, with static polymorphism it is determined compile-time.

There's no need to consider static and dynamic polymorphism as mutually exclusive variants of polymorphism. Rather, both can be used together, combining their strengths.

This section contains several subsections.

22.12.1: An example of static polymorphism

With static polymorphism a class template takes the role of a base class in dynamic polymorphism. This class template declares several members, which are comparable to the members of a polymorphic base class: they are either support members or they are interfacing to members overridden in derived classes.

With dynamic polymorphism these overriding members are the base class's virtual members. With static polymorphism there are no virtual members. Instead, the statically polymorphic base class (referred to as the `base class' below) declares a template type parameter (referred to as the `derived class type' below). Next, the base class's interfacing members call members of the derived class type.

Here is an example of a simple class template which will be used as a base class. Its public interface consists of one member, and, different from dynamic polymorphism, there's no reference in the class's interface to any members showing polymorphic behavior: 

    template <class Derived>
    struct Base
    {
        void interface();
    }

Let's have a closer look at the member `interface'. This member is called by functions receiving a reference or pointer to the base class, and it calls members that must be available in the derived class type. Before we can call members of the derived class type an object of the derived class type must be available. This object is obtained through inheritance. The derived class type is going to be derived from the base class. Thus Base's this pointer is also Derived's this pointer.

When we have a class Derived: public Base then a static_cast<Derived *> can be used to cast a Base * that is actually pointing to a Derived object. A dynamic_cast of course doesn't apply, as we don't use dynamic polymorphism. A static_cast is appropriate since our Base * does in fact point to a Derived class object.

Consequently, to call a Derived class member from within interface we can use the following implementation: 

    template<class Derived>
    void Base<Derived>::interface()
    {
        static_cast<Derived *>(this)->polymorphic();
    }
Interestingly, when the compiler is given this implementation it cannot determine whether Derived is actually derived from Base. Neither can it determine whether the class Derived indeed offers a member polymorphic. The compiler simply assumes this to be true, in which case the provided implementation is syntactically correct. One of the core characteristics of using templates is that the implementation's viability is eventually determined at the function's point of instantiation (cf. section 21.6).

Consequently, in order to use the above scheme we must ensure that derived class types are actually derived from the base class and that the derived class types actually define a member `polymorphic'. The first requirement is satisfied using the curiously recurring template pattern: 

    class First: public Base<First>
In this curious pattern the class First is derived from Base, which itself is instantiated for First. This is acceptable, as the compiler already has determined that the type First exists. At this point that is all it needs.

The second requirement is satisfied by providing an implementation of the member polymorphic. In chapter 14 we saw that virtual and overriding members belong to the class's private interface. Applying the same philosophy here, we put polymorphic in First's private interface, allowing its access by the base class by declaring 

    friend void Base<First>::interface();

First's complete class interface can now be designed, followed by polymorphic's implementation: 

    class First: public Base<First>
    {
        friend void Base<First>::interface();

        private:
            void polymorphic();
    };
    void First::polymorphic()
    {
        std::cout << "polymorphic from First" << std::endl;
    }
Note that the class First itself is not a class template: its members can be separately compiled and stored in, e.g., a library. Also, as is the case with dynamic polymorphism, the member polymorphic has full access to all of First's data members and member functions.

Multiple classes can now be designed like First, each offering their own implementation of polymorphic. E.g., the member Second::polymorphic of the class Second, designed like First, could be implemented like this: 

    void Second::polymorphic()
    {
        std::cout << "polymorphic from Second" << std::endl;
    }

The polymorphic nature of Base becomes apparent once a function template is defined in which Base::interface is called. Again, the compiler simply assumes a member interface exists when it reads the definition of the following function template: 

    template <class Class>
    void fun(Class &object)
    {
        object.interface();
    }

Only at the point where this function is actually called will the compiler verify the viability of the generated code. In the following main function a First object is passed to fun: First declares interface through its base class, and First::polymorphic is called by interface. Then a Second object is passed to fun, and analogously Second::polymorphic is called: 

    int main()
    {
        First first;
        fun(first);

        Second second;
        fun(second);
    }

There are also downsides to using static polymorphism. First, the sentence `a Second object is passed to fun' isn't really correct, since fun in fun(first) and fun(second) are different functions, not just calls of one function with different arguments. With static polymorphism every instantiation using its own template parameters results in completely new code once the template (e.g., fun) is instantiated. This is something to consider when creating statically polymorphic base classes. If the base class defines data members and member functions, and if these additional members are used by derived class types, then each member will have its own instantiation for each derived class type. This also represents code bloat, albeit of a different kind than obeserved with dynamic polymorphism. This kind of code bloat can often be somewhat reduced by deriving the base class from its own (ordinary) base class, encapsulating all elements of the statically polymorphic base class that do not depend on its template type parameter.

Second, if different types of statically polymorphic objects are dynamically created then the types of the returned pointers are all different, as are the types of the pointers to their statically polymorphic base classes. These latter pointers are different because they are pointers to Base<Derived>, representing different types for different Derived types. Consequently, and different from dynamic polymorphism, these pointers cannot be collected in, e.g., a vector of shared pointers to base class pointers. There simply isn't one base class pointer type. Thus, because of the different base class types, there's no direct statically polymorphic equivalent to virtual destructors.

Third, as will be illustrated in the next section, designing static polymorphic classes using multiple levels of inheritance is not a trivial task.

Summarizing, static polymorphism is best used in cases where a limited number of different derived class types are defined, where a fixed number of derived class objects are used, and where the statically polymorphic base classes themselves are lean (possibly encapsulating some of their code in ordinary base classes of their own).

22.12.2: Converting dynamic polymorphic classes to static polymorphic classes

So you've decided to convert some of your dynamically polymorphic classes into statically polymorphic classes. How to realize the conversion?

In chapter 14 the base class Vehicle and some derived classes were introduced. Vehicle, Car and Truck's interfaces look like this (concentrating on the members that are involved in their polymorphic behavior): 

    class Vehicle
    {
        size_t d_massFactor;

        public:
            int mass() const;
            int si_mass() const;

        private:
            virtual int vmass() const;
    };

    class Car: public Vehicle
    {
        size_t d_mass;
        private:
            int vmass() const override;
    };
        
    class Truck: public Car
    {
        size_t d_mass;
        private:
            int vmass() const override;
    };
Thee members of the user-interface were implemented like this: 
    int Vehicle::mass() const
    {
        return d_massFactor * si_mass();
    }
    int Vehicle::si_mass() const
    {
        return vmass();
    }

When converting dynamically polymorphic classes to statically polymorphic classes we must realize that polymorphic classes serve two functions: first, they define facilities (data members, member functions) that are inherited by derived classes, and second polymorphic classes implement the redefinable interface in a way that fits their purpose.

With statically polymorphic classes it is important that these two aspects are implemented separately. As we've seen in the previous section, a statically polymorphic derived class derives from the base class by using its own class type as argument to the base class's type parameter. This works fine if there's only one level of inheritance.

With multiple levels of inheritance (e.g., Truck -> Car -> Vehicle) Truck's inheritance specification becomes a problem. If it is inheriting from Car, then it implicitly derives from Vehicle<Car>, and thus Car's vmass is called by Vehicle::interface. But Truck must inherit from Car to be able to use Car's features. Additionally inheriting Truck from Vehicle<Truck> isn't an option either, as this creates a class Truck which also inherits from Vehicle<Car> (through Truck's Car base class).

Figure 26 is shown here.
Figure 26: Vehicle Static Polymorphic Class Design

Generally it cannot be ruled out that classes use multiple levels of inheritance. When static polymorphism is used classes must carefully be designed. By separating the redefinable interface from the other elements of the interface, the normal line of inheritance is used to make the protected and public interfaces of (direct or indirect) base classes available to a derived class. The left-hand side of figure 26 shows this line of inheritance. Each of the left-hand side classes is then used as a base class, together with the static polymorhic base class, to create a statically polymorphic derived class defining its own implementation of the static base class's redefinable interface. The right-hand side of of figure 26 shows this part of the design. The XBase classes in the left-hand side of figure 26 contain the non-redefinable elements of the original dynamically polymorphic classes. They should of course still be available to the statically polymorphic classes (shown in the right-hand side of figure 26). This is realized using friend declarations: the XBase classes declare `friend class X', after which XBase essentially has become part of the class X.

Now that we've analyzed the design of statically polymorphic classes using multiple levels of inheritance we're ready for the conversion of the Vehicle, Car, and Truck dynamically polymorphic classes to statically polymorphic classes. To concentrate on the actual conversion process the design of the classes is kept simple. E.g., usually appearing elements like constructors were not included in the examples. Furthermore, to save some space all implementations of member functions are provided in-class.

First the class Vehicle. Vehicle's non-redifinable interface is moved to a class VehicleBase, and Vehicle itself is turned into a statically polymorphic base class. Here only Vehicle::d_massFactor needs to be moved to VehicleBase. But in general all members of the original dynamically polymorphic base class that do not use or implement virtual members should be moved to the XBase class. VehicleBase also declares Vehicle to be its friend, so Vehicle is not denied access to its members, now living in VehicleBase. Here is VehicleBase: 

    class VehicleBase
    {
        // original Vehicle members, not implementing the
        // redefinable interface 

        template <class Derived>
        friend class Vehicle;

        size_t d_massFactor = 1;
    };

The statically polymorphic Vehicle base class implements the redefinable interface. All other facilities are in VehicleBase, from which it is derived. Here is VehicleBase: 

    template <class Derived>
    class Vehicle: public VehicleBase
    {
        public:
            int mass() const
            {
                return d_massFactor *
                        static_cast<Derived const *>(this)->vmass();
            }
    };
In this implementation Vehicle does not implement its own vmass member. We cannot define Vehicle<Vehicle>, and with static polymorphism the base class is essentially comparable to an abstract base class. If this is not required, then a default class can be specified for Vehicle's Derived class, implementing the redefinable interface of the original dynamically polymorphic base class (allowing definitions like Vehicle<> vehicle).

Likewise the class Car is split into CarBase and Car. CarBase uses standard inheritance to inherit VehicleBase's protected and public interface. Here is its implementation, adding a private data member for illustration purposes: 

    class CarBase: public VehicleBase
    {
        // original Car members, not implementing the
        // redefinable interface 

        int x = 1000;
        friend class Car;
    };

The class Car receives CarBase's members through inheritance. Furthermore, it inherits from Vehicle<Car>, implementing its own version of Vehicle's redefinable interface. Note the specific friend declaration, allowing Vehicle<Car> to access Car's private vmass member: 

    class Car: public CarBase, public Vehicle<Car>
    {
        friend class Vehicle<Car>;

        int vmass() const
        {
           return x;
        }
    };

This design pattern can be used for deeper levels of inheritance as well. Once more we need to split a polymorphic class into two separate classes: the polymorphic class Truck is split into TruckBase and a statically polymorphic class Truck, implementing Vehicle's redefinable interface. Here is TruckBase, inheriting from CarBase, and thus also from VehicleBase: 

    class TruckBase: public CarBase
    {
        // original Truck members, not implementing the
        // redefinable interface 

        friend class Truck;
    };

Finally, we finish our class conversion for the class Truck, now implementing its own version of the statically polymorphic class Vehicle: 

    class Truck: public TruckBase, public Vehicle<Truck>
    {
        friend class Vehicle<Truck>;

        private:
            int vmass() const
            {
                return 15000;
            }
    };

The original function void fun(Vehicle &vehicle) still needs to be converted to a function template. Here is its definition: 

    template <class Vehicle>
    void fun(Vehicle &vehicle)
    {
        cout << vehicle.mass() << '\n';
    }
Note that Vehicle is just a formal name. When an object is passed to fun it must offer a member mass, or compilation will fail. If the object is in fact a Car or Truck, then their Vehicle<Type> static base class member mass is called, which in turn uses static polymorphism to call the member vmass as implemented by the actually passed class type. The following main function displays, respectively, 1000 and 15000: 
    int main()
    {
        Car car;
        fun(car);
    
        Truck truck;
        fun(truck);
    }
Realize that this program implements fun twice, rather than once in the case of dynamic polymorphism. The same holds true for the Vehicle class template: two implementations, one for the Car type, and one for the Truck type. The statically polumorphic program will be slightly faster, though.

22.12.3: Using static polymorphism to avoid reimplementations

Static polymorphism may profitably be used to avoid reimplementing code in an otherwise dynamic polymorphic environment.

Consider the situation where we have a class containing a container of pointers to some polymorphic base class type (like the class Vehicle from chapter 14). How to copy such a container to another container? We're not hinting at using shared pointers here, but would like to make a full copy. Clearly, we'll need to duplicate the objects the pointers point at, and assign these new pointers to the copied object's container.

The prototype design patttern is commonly used to create copies of objects of polymorphic classes, given pointers to their base classes.

To apply the prototype design pattern we have to implement newCopy in all derived classes. Not by itself a big deal, but static polymorphism can nicely be used here to avoid having to reimplement this function for each derived class.

We start off with an abstract base class VehicleBase declaring a pure virtual member newCopy: 

    struct VehicleBase
    {
        virtual ~VehicleBase();
        VehicleBase *clone() const; // calls newCopy

        // declare any additional members defining the 
        // public user interface here

        private:
            VehicleBase *newCopy() const = 0;   
    };

Next we define a static polymorphic class CloningVehicle which is derived from VehicleBase (note that we thus combine dynamic and static polymorphism). This class provides the generic implementation of newCopy. This is possible because all derived classes can use this implementation. Also, CloningVehicle will be re-implemented for each concrete type of vehicle that is eventually used: a Car, a Truck, an AmphibiousVehicle, etc, etc. CloningVehicle thus isn't shared (like VehicleBase), but instantiated for each new type of vehicle.

The core characteristic of a statically polymorphic class is that it can use its class template type parameter via a static_cast of its own type. A member function like newCopy is implemented always the same way, viz., by using the derived class's copy constructor. Here is the class CloningVehicle: 

    template <class Derived>
    class CloningVehicle: public VehicleBase
    {
        VehicleBase *newCopy() const
        {
            return new Derived(*static_cast<Derived const *>(this));
        }
    };

And we're done. All types of vehicles should now be derived from CloningVehicle, which automatically provides them with their own implementation of newCopy. E.g., a class Car looks like this: 

    class Car: public CloningVehicle<Car>
    {
        // Car's interface, no need to either
        // declare or implement newCopy,
        // but a copy constructor is required.
    };

Having defined a std::vector<VehicleBase *> original we could create a copy of original like this: 

    for(auto pointer: original)
        duplicate.push_back(pointer->clone());
Irrespective of the actual type of vehicle to which the pointers point, their clone members will return pointers to newly allocated copies of objects of their own types.

22.13: Class templates and nesting

When a class is nested within a class template, it automatically becomes a class template itself. The nested class may use the template parameters of the surrounding class, as shown by the following skeleton program. Within a class PtrVector, a class iterator is defined. The nested class receives its information from its surrounding class, a PtrVector<Type> class. Since this surrounding class should be the only class constructing its iterators, iterator's constructor is made private and the surrounding class is given access to the private members of iterator using a bound friend declaration. Here is the initial section of PtrVector's class interface: 
    template <typename Type>
    class PtrVector: public std::vector<Type *>

This shows that the std::vector base class stores pointers to Type values, rather than the values themselves. Of course, a destructor is now required as the (externally allocated) memory for the Type objects must eventually be freed. Alternatively, the allocation might be part of PtrVector's tasks, when it stores new elements. Here it is assumed that PtrVector's clients do the required allocations and that the destructor is implemented later on.

The nested class defines its constructor as a private member, and allows PtrVector<Type> objects access to its private members. Therefore only objects of the surrounding PtrVector<Type> class type are allowed to construct their iterator objects. However, PtrVector<Type>'s clients may construct copies of the PtrVector<Type>::iterator objects they use.

Here is the nested class iterator, using a (required) friend declaration. Note the use of the typename keyword: since std::vector<Type *>::iterator depends on a template parameter, it is not yet an instantiated class. Therefore iterator becomes an implicit typename. The compiler issues a warning if typename has been omitted. Here is the class interface: 

            class iterator
            {
                friend class PtrVector<Type>;
                typename std::vector<Type *>::iterator d_begin;

                iterator(PtrVector<Type> &vector);

                public:
                    Type &operator*();
            };

The implementation of the members shows that the base class's begin member is called to initialize d_begin. PtrVector<Type>::begin's return type must again be preceded by typename: 

    template <typename Type>
    PtrVector<Type>::iterator::iterator(PtrVector<Type> &vector)
    :
        d_begin(vector.std::vector<Type *>::begin())
    {}

    template <typename Type>
    Type &PtrVector<Type>::iterator::operator*()
    {
        return **d_begin;
    }

The remainder of the class is simple. Omitting all other functions that might be implemented, the function begin returns a newly constructed PtrVector<Type>::iterator object. It may call the constructor since the class iterator declared its surrounding class as its friend: 

    template <typename Type>
    typename PtrVector<Type>::iterator PtrVector<Type>::begin()
    {
        return iterator(*this);
    }

Here is a simple skeleton program, showing how the nested class iterator might be used: 

    int main()
    {
        PtrVector<int> vi;

        vi.push_back(new int(1234));

        PtrVector<int>::iterator begin = vi.begin();

        std::cout << *begin << '\n';
    }

Nested enumerations and nested typedefs can also be defined by class templates. The class Table, mentioned before (section 22.11.3) inherited the enumeration TableType::FillDirection. Had Table been implemented as a full class template, then this enumeration would have been defined in Table itself as: 

    template <typename Iterator>
    class Table: public TableType
    {
        public:
            enum FillDirection
            {
                HORIZONTAL,
                VERTICAL
            };
        ...
    };
In this case, the actual value of the template type parameter must be specified when referring to a FillDirection value or to its type. For example (assuming iter and nCols are defined as in section 22.11.3): 
    Table<istream_iterator<string> >::FillDirection direction =
                argc == 2 ?
                    Table<istream_iterator<string> >::VERTICAL
                :
                    Table<istream_iterator<string> >::HORIZONTAL;

    Table<istream_iterator<string> >
        table(iter, istream_iterator<string>(), nCols, direction);

22.14: Constructing iterators

In section 18.2 the iterators used with generic algorithms were introduced. We've seen that several types of iterators were distinguished: InputIterators, ForwardIterators, OutputIterators, BidirectionalIterators and RandomAccessIterators.

To ensure that an object of a class is interpreted as a particular type of iterator, the class must be derived from the class std::iterator. Before a class can be derived from this class the <iterator> header file must be included.

In section 18.2 the characteristics of iterators were discussed. All iterators should support (using Iterator as the generic name of the designed iterator class and Type to represent the (possibly const, in which case the associated operator should be a const member as well) data type to which Iterator objects refer):

When iterators are to be used in the context of generic algorithms they must meet additional requirements. This is caused by the fact that generic algorithms perform checks on the types of the iterators they receive. Simple pointers are usually accepted, but if an iterator-object is used it must be able to specify the kind of iterator it represents.

When deriving a class from the class iterator the type of iterator is defined by the class template's first parameter, and the data type to which the iterator refers is defined by the class template's second parameter.

The type of iterator that is implemented by the derived class is specified using a so-called iterator_tag, provided as the first template argument of the class iterator. For the five basic iterator types, these tags are:

Each iterator tag assumes that a certain set of operators is available. The RandomAccessIterator is the most complex of iterators, as it implies all other iterators.

Note that iterators are always defined over a certain range ([begin, end)). Increment and decrement operations may result in undefined behavior of the iterator if the resulting iterator value would refer to a location outside of this range.

Often, iterators only access the elements of the series to which they refer. Internally, an iterator may use an ordinary pointer but it is hardly ever necessary for the iterator to allocate its own memory. Therefore, as the assignment operator and the copy constructor do not have to allocate any memory, their default implementations usually suffice. For the same reason iterators usually don't require destructors.

Most classes offering members returning iterators do so by having members construct the required iterators that are thereupon returned as objects by those member functions. As the caller of these member functions only has to use or sometimes copy the returned iterator objects, there is usually no need to provide any publicly available constructor, except for the copy constructor. Therefore these constructors are usually defined as private or protected members. To allow an outer class to create iterator objects, the iterator class usually declares the outer class as its friend.

In the following sections the construction of a RandomAccessIterator, the most complex of all iterators, and the construction of a reverse RandomAccessIterator is discussed. The container class for which a random access iterator must be developed may actually store its data elements in many different ways (e.g., using containers or pointers to pointers). Therefore it is difficult to construct a template iterator class which is suitable for a large variety of container classes.

In the following sections the available std::iterator class is used to construct an inner class representing a random access iterator. The reader may follow the approach illustrated there to construct iterator classes for other contexts. An example of such a template iterator class is provided in section 24.7.

The random access iterator developed in the next sections reaches data elements that are only accessible through pointers. The iterator class is designed as an inner class of a class derived from a vector of string pointers.

22.14.1: Implementing a `RandomAccessIterator'

In the chapter about containers (chapter 12) it was noted that containers own the information they contain. If they contain objects, then those objects are destroyed once the containers are destroyed. As pointers are not objects their use in containers is discouraged (STL's unique_ptr and shared_ptr type objects may be used, though). Although discouraged, we might be able to use pointer data types in specific contexts. In the following class StringPtr, an ordinary class is derived from the std::vector container that uses std::string * as its data type: 
    #ifndef INCLUDED_STRINGPTR_H_
    #define INCLUDED_STRINGPTR_H_

    #include <string>
    #include <vector>

    class StringPtr: public std::vector<std::string *>
    {
        public:
            StringPtr(StringPtr const &other);
            ~StringPtr();

            StringPtr &operator=(StringPtr const &other);
    };

    #endif

This class needs a destructor: as the object stores string pointers, a destructor is required to destroy the strings once the StringPtr object itself is destroyed. Similarly, a copy constructor and overloaded assignment is required. Other members (in particular: constructors) are not explicitly declared here as they are not relevant to this section's topic.

Assume that we want to be able to use the sort generic algorithm with StringPtr objects. This algorithm (see section 19.1.58) requires two RandomAccessIterators. Although these iterators are available (via std::vector's begin and end members), they return iterators to std::string *s, which cannot sensibly be compared.

To remedy this, we may define an internal type StringPtr::iterator, not returning iterators to pointers, but iterators to the objects these pointers point to. Once this iterator type is available, we can add the following members to our StringPtr class interface, hiding the identically named, but useless members of its base class: 

    StringPtr::iterator begin();    // returns iterator to the first element
    StringPtr::iterator end();      // returns iterator beyond the last
                                    // element
Since these two members return the (proper) iterators, the elements in a StringPtr object can easily be sorted: 
    int main()
    {
        StringPtr sp;               // assume sp is somehow filled

        sort(sp.begin(), sp.end()); // sp is now sorted
    }
To make this all work, the type StringPtr::iterator must be defined. As suggested by its type name, iterator is a nested type of StringPtr. To use a StringPtr::iterator in combination with the sort generic algorithm it must also be a RandomAccessIterator. Therefore, StringPtr::iterator itself must be derived from the existing class std::iterator.

To derive a class from std::iterator, both the iterator type and the data type the iterator points to must be specified. Caveat: our iterator takes care of the string * dereferencing; so the required data type is std::string, and not std::string *. The class iterator therefore starts its interface as: 

    class iterator:
        public std::iterator<std::random_access_iterator_tag, std::string>
Since its base class specification is quite complex, we could consider associating this type with a shorter name using the following typedef: 
    typedef std::iterator<std::random_access_iterator_tag, std::string>
            Iterator;
In practical situations, if the type (Iterator) is used only once or twice, the type definition only adds clutter to the interface, and is better not used.

Now we're ready to redesign StringPtr's class interface. It offers members returning (reverse) iterators, and a nested iterator class. Here is its interface: 

class StringPtr: public std::vector<std::string *>
{
    public:
    class iterator: public
            std::iterator<std::random_access_iterator_tag, std::string>
    {
        friend class StringPtr;
        std::vector<std::string *>::iterator d_current;

        iterator(std::vector<std::string *>::iterator const &current);

        public:
            iterator &operator--();
            iterator operator--(int);
            iterator &operator++();
            iterator operator++(int);
            bool operator==(iterator const &other) const;
            bool operator!=(iterator const &other) const;
            int operator-(iterator const &rhs) const;
            std::string &operator*() const;
            bool operator<(iterator const &other) const;
            iterator operator+(int step) const;
            iterator operator-(int step) const;
            iterator &operator+=(int step); // increment over `n' steps
            iterator &operator-=(int step); // decrement over `n' steps
            std::string *operator->() const;// access the fields of the
                                            // struct an iterator points
                                            // to. E.g., it->length()
    };

    typedef std::reverse_iterator<iterator> reverse_iterator;

    iterator begin();
    iterator end();
    reverse_iterator rbegin();
    reverse_iterator rend();
};

As usual, the interface offers hooks for a more detailed study of the class.

First we have a look at StringPtr::iterator's characteristics:

The interfaces required for other iterator types are simpler, requiring only a subset of the interface required by a random access iterator. E.g., the forward iterator is never decremented and never incremented over arbitrary step sizes. Consequently, in that case all decrement operators and operator+(int step) can be omitted from the interface. Of course, the tag to use would then be std::forward_iterator_tag. The tags (and the set of required operators) vary accordingly for the other iterator types.

22.14.2: Implementing a `reverse_iterator'

Once we've implemented an iterator, the matching reverse iterator can be implemented in a jiffy. Comparable to the std::iterator a std::reverse_iterator exists, that nicely implements the reverse iterator for us once we have defined an iterator class. Its constructor merely requires an object of the iterator type for which we want to construct a reverse iterator.

To implement a reverse iterator for StringPtr we only need to define the reverse_iterator type in its interface. This requires us to specify only one line of code, which must be inserted after the interface of the class iterator: 

    typedef std::reverse_iterator<iterator> reverse_iterator;
Also, the well known members rbegin and rend are added to StringPtr's interface. Again, they can easily be implemented inline: 
inline StringPtr::reverse_iterator StringPtr::rbegin()
{
    return reverse_iterator(end());
}
inline StringPtr::reverse_iterator StringPtr::rend()
{
    return reverse_iterator(begin());
}

Note the arguments the reverse_iterator constructors receive: the begin point of the reversed iterator is obtained by providing reverse_iterator's constructor with the value returned by the member end: the endpoint of the normal iterator range; the endpoint of the reversed iterator is obtained by providing reverse_iterator's constructor with the value returned by the member begin: the begin point of the normal iterator range.

The following small program illustrates the use of StringPtr's RandomAccessIterator: 

    #include <iostream>
    #include <algorithm>
    #include "stringptr.h"
    using namespace std;

    int main(int argc, char **argv)
    {
        StringPtr sp;

        while (*argv)
            sp.push_back(new string(*argv++));

        sort(sp.begin(), sp.end());
        copy(sp.begin(), sp.end(), ostream_iterator<string>(cout, " "));

        cout << "\n======\n";

        sort(sp.rbegin(), sp.rend());
        copy(sp.begin(), sp.end(), ostream_iterator<string>(cout, " "));

        cout << '\n';
    }
    /*
            when called as:
        a.out bravo mike charlie zulu quebec

            generated output:
        a.out bravo charlie mike quebec zulu
        ======
        zulu quebec mike charlie bravo a.out
    */

Although it is thus possible to construct a reverse iterator from a normal iterator, the opposite does not hold true: it is not possible to initialize a normal iterator from a reverse iterator.

Assume we would like to process all lines stored in vector<string> lines up to any trailing empty lines (or lines only containing blanks) it might contain. How should we proceed? One approach is to start the processing from the first line in the vector, continuing until the first of the trailing empty lines. However, once we encounter an empty line it does of course not have to be the first line of the set of trailing empty lines. In that case, we'd better use the following algorithm:

However, we can't mix iterators and reverse iterators when using generic algorithms. So how can we initialize the second iterator using the available reverse_iterator? The solution is not very difficult, as an iterator may be initialized from a pointer. Although the reverse iterator rit is not a pointer, &*(rit - 1) or &*--rit is. So we use 
    for_each(lines.begin(), &*--rit, Process());
to process all the lines up to the first of the set of trailing empty lines. In general, if rit is a reverse_iterator pointing to some element and we need an iterator to point to that element, we may use &*rit to initialize the iterator. Here, the dereference operator is applied to reach the element the reverse iterator refers to. Then the address operator is applied to obtain its address with which we can initialize the iterator.

When defining a const_reverse_iterator (e.g., matching a const_iterator class), then the const_iterator's operator* member should be a member returning a non-modifiable value or object. Since a const_reverse_iterator uses the iterator's operator-- member, we're running against a small conceptual conflict. On the one hand, a std::input_iterator_tag is inappropriate, since we must allow decrementing the iterator. On the other hand, a std::bidirectional_iterator is inappropriate, since we don't allow modification of the data.

Iterator tags are primarily conceptual. If const_iterators and const_reverse_iterators only allow increment operations, then an input_iterator_tag most closely matches the iterator's intended use. Hence this tag is used below.

Furthermore, in line with the nature of a input_iterator_tag our const_iterator should not offer an operator--. This, of course, causes problems: a reverse iterator must be able to use the iterator's operator-- member. This can easily be solved by stashing the iterator's operator-- in the iterator's private section, and declaring std::reverse_iterator<(const_)iterator> its friend (note that declaring a (const_)reverse_iterator that is derived from std::reverse_iterator doesn't solve the issue: it is std::reverse_iterator that calls the iterator's operator--, not a class that is derived from it).

There is, however, another issue. After deriving a const_reverse_iterator from const_iterator, and subsequently dereferencing a const_reverse_iterator, the compiler generates an error message like the following (using Type = int): 

error: invalid initialization of non-const reference of type
'std::reverse_iterator<const_iterator>::reference {aka int&}' from an rvalue
of type 'int' 
  return *--__tmp;

This message is caused by std::reverse_iterator by default expecting that the iterator's operator* returns a reference to a modifiable Type.

To control such default expectancies, iterators can use typedefs to fine-tune these expectancies. The following typedefs are interpreted by std::reverse_iterator: 

    pointer         -   the type of the pointer to the data 
                        (e.g., Type *)
    const_pointer   -   the type of a pointer to immutable data
                        (e.g., Type const *)
    reference       -   the type of a reference to the data
                        (e.g., Type &)
    const_reference -   the type of a reference to immmutable data
                        (e.g., Type const &)
    difference_type -   the type representing differences between
                        pointers (by default `ptrdiff_t')

The mentioned error can simply be prevented by declaring `typedef int const &reference' in the iterator class. Alternatively, int const may be specified as the data type for the std::iterator's base class.

To define a iterator, const_iterator, reverse_iterator and const_reverse_iterator for a class Data the following framework can be used: 

#include <string>
#include <iterator>

class Data
{
    std::string *d_data;
    size_t d_n;

    public:
        class iterator;
        class const_iterator;

        typedef std::reverse_iterator<iterator> reverse_iterator;
        typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
};

class Data::iterator: public std::iterator<std::input_iterator_tag,
                                           std::string>
{
    public:
        iterator() = default;

        iterator &operator++();
        std::string &operator*();

    private:
        friend class Data;
        iterator(std::string *data, size_t idx);

        friend class std::reverse_iterator<iterator>;
        iterator &operator--();
};

bool operator==(Data::iterator const &lhs, Data::iterator const &rhs);



class Data::const_iterator: public std::iterator<std::input_iterator_tag,
                                                 std::string const>
{
    public:
        const_iterator() = default;

        const_iterator &operator++();
        std::string const &operator*() const;

    private:
        friend class Data;
        const_iterator(std::string const *data, size_t idx);

        friend class std::reverse_iterator<const_iterator>;
        const_iterator &operator--();
};

bool operator==(Data::const_iterator const &lhs,
                Data::const_iterator const &rhs);


int main()
{
    Data::iterator iter;
    Data::reverse_iterator riter(iter);

    *riter;

    Data::const_iterator citer;
    Data::const_reverse_iterator criter(citer);

    *criter;

};