Title: Tiny Template Tidbit

I am constantly amazed at what can be done with templates. I started programming in C around 1985 and in C++ only around 1995. Most of my work over the past 6 years has involved using C++ to the maximum of my abilities, but only for three years have I been working with templates. In this article I would like to share a very small template tidbit, something I think is really cool. I hope it can stimulate your interest in using template capabilities for your own code, or just be another "trick" to put in your bag, something I think fairly easy to remember.

I will assume in this article that you are at least familiar with a few of the STL class templates, and, though you may not have written your own class templates before, you have "seen how it's done".

We have an application in which a set of objects is being generated by a third-party library and stored in a container. For simplicity, I will refer to the objects as "points". Objects of this class don't necessarily have much intrinsic behavior, and are used by other classes of objects or functions for complex computations. For instance, an object (which I call a processor for clarity) might use the set of points to create a spline curve that best fits the points. That is, each point is simply a 2D coordinate, an aggregate of two numbers:

struct Point {float x,y;};
std::set<Point> points;

Yet, as the application evolves, it is likely that objects of the Point class will become more complex. Perhaps other state data, such as local temperature, contact normal, density, etc, will be "carried around" along with the coordinates of the point. In this case, the Point class suddenly changes from being the data to being an aggregate of a data object and the other state data:

struct Coord {float x,y;};
        // coordinates in 2D space
struct Vec {float x,y;};
        // vector in 2D space
struct Point {
  Coord coords;
        // the coordinate pair of the point
  Vec contactNormal;
        // new state data associated with point
  float temperature, density;
       // other state data...
};
std::set<Point> points;

The "curve fitter" processor mentioned earlier suddenly no longer works since it was designed to use the point as a 2D coordinate pair, not as an object containing the 2D coordinate pair as a data member.

Assuming the curve-fitter could be designed to compile in both cases, the application may evolve such that the 2D coordinates of the point are no longer a publicly accessible attribute, but rather a private data member than can only be accessed via a const "get" method (or even computed on-the-fly instead of being a data member). This could happen when Point starts having behavior of its own, not necessarily relevant to the curve-fitting operation of the processor. Since the latter was designed to access an attribute, it no longer accepts the new class of Point. For instance,

struct Foo1 {int bar;};
struct Foo2 {int bar() const;};

Both should be adequate for the curve-fitter, yet the latter would fail to compile if Foo2 is used instead of Foo1, complaining that bar() is not an attribute (or some equivalent hard-to-decode error message, different for every compiler). Does the processor really care how the data is acquired?

If this weren't enough, the container type may change, yet the processor object (curve-fitter in this example) does not care: a std::vector, a std::list, a std::set, or a your::container, as long as the data is there, the processor should be satisfied. This is trivial to adapt to, as you will see below, but more importantly, what if the container stores pointers to the points rather than the actual points? This is likely to happen if copying Point is onerous and you need to avoid copying those objects in your application, so you change the container type from containing Point to containing Point*. Suddenly, the curve-fitter no longer compiles since it expects each element of the container to be an object, not a pointer to an object.

Finally, our processor (object or function) may be used in different modules, or even different applications we build, perhaps for related yet distinct application domains. Do we want to have 10 different versions of the same code, one for each possible container type and point design?

It turns out that templates can be used in C++ to make one processor (object or function) that accepts any container that uses iterators AND, much more interestingly, is able to extract the needed data from the container elements, regardless of whether the container element type

Moreover, templates allow you to do so at compile time, and automatically, without your intervention. Yep, no kidding! Hopefully, you can see that the above is a fairly generic problem, unrelated to the particular application domain (curve-fitting) in which I encountered it.

Let's start simple and try to keep things simple. Assume we have a function called fitCurve that takes a container of points and finds the curve that best fits the set, returning the result as a Curve object. We are not concerned with the definition of the Curve class. To be generic, let's call the point class Coord and the container of points Coords:

#include "Curve.hh"
#include "Coord.hh"
typedef std::list<Coord> Coords;
Curve fitCurve(const Coord& coords);

This function can be used only to fit a curve to a set of Coord objects stored in a std::list. If you have a set of Coords in a std::set or a std::vector, fitCurve cannot be used. Why should the interface force us to use one type, when fitCurve only cares that the set is ordered? If you want to use STL containers, then the containers are not related by inheritance, but they do share common interfaces for certain operations. For instance, they all have an iterator type nested. Let's make fitCurve independent of the container type. We use templates to parameterize fitCurve on the container type, for instance

// note: syntax wrong but you get the idea:
template <class Container>
Curve fitCurve(const Container<Coord>& coords)
{
  // ...
  // set coord1 to first Coord in coords
  // set coord2 to second Coord in coords
  Coord c = coord1 + coord2;
  // ...
}

The only requirement on the element type (Coord) in the container is that it have an operator+ defined. The requirement on the container is that we use Container::iterator instead of other access operators such as operator[] to access the individual elements of the container.

What are some of the advantages and disadvantages of parameterizing? I can think of the following:

Any kind of container, whose concrete type is known at compile time, can be given to the curve fitter. For each new type of container, the compiler takes the "function template" (i.e. a template for a function) and generates a "template function" (i.e. a function that comes from a template) - the order of those words matters. There will be a few constraints on the operations required from the container, but this is already far better than being stuck with one container class. The alternative would be to copy all the elements from your container to the container expected by fitCurve.

Since fitCurve is a function, most compilers will know to generate the template function for the given container without your having to specify it explicitly. The mere act of calling fitCurve with your container is enough, since the compiler knows the type of container you are using, and can generate the template function automatically.

For the same reason, you can change the type of your container at some later stage of development, without having to do anything to fitCurve: the compiler and your build environment will know that the old "template function" should be changed to a new one, at compilation time, and will do the change for you.

Every template function that is generated by the compiler means extra code. This is the famous "code bloat" problem of class and function templates. This is a factor to consider only if you plan on using several different containers in the same application (which is not necessarily the case), and memory footprint matters.

It can be difficult to predict how "well behaved" is the Container (template) class. Can it throw exceptions? Does its interface properly identify what is const and non-const? Can this invalidate the algorithm that accesses the Container? There will always be cases where the disadvantages outweigh the advantages, but I have found the reverse to be true much more often.

The next step is to allow the container element type to be a pointer to a Coord as well as a Coord. Intuitively, we know it should be possible: the compiler knows exactly what is the type of what is contained: i.e., a Coord or a pointer to a Coord. When the element type is a pointer to Coord, the above piece of code would have coord1 and coord2 be pointers to Coord objects rather than actual Coord objects. Wouldn't it be nice if we could write, in the above code, something like:

const Coord& c1 = getCoord(coord1);
const Coord& c2 = getCoord(coord2);
Coord sum = c1 + c2;

If the element type is a Coord, then getCoord(coord1) just returns coord1. If on the other hand it is a Coord*, then getCoord(coord1) returns *coord1. Simple overloading allows us to do that:

const Coord& getCoord(const Coord& v)
  {return v;}
const Coord& getCoord(const Coord* v)
  {return *v;}

Now things are going to get a little more interesting. We want to allow the element type of the container be something else than a Coord, i.e. it could be a Point that contains a Coord. All we need is to overload getCoord() once more for the case where v is a Point:

const Coord& getCoord(const Point& v)
  {return v.coords;}

Of course, we want to be able to use our own class instead of Point. Templates come to the rescue once again:

template <class POINT>
const Coord& getCoord(const POINT& v)
  {return v.coords;}

This requires that POINT, the type of object contained by Container in fitCurve, have a publicly visible "coords" data member. So it's not totally generic but again, far better than being stuck with only Point and Coord objects!

Before dealing with the member "attributes vs. methods" problem, the last requirement is that the container can contain pointers to point types that contain the Coord data as a data member. What we need is a template overload for pointers:

template <class POINT>
const Coord& getCoord(const POINT* p)
  {return p->coords;}

It is somewhat like "partial specialization" because some of the type information is still general and unknown (POINT could be anything) but some is specific: it must be a pointer to something. However "partial specialization" specifically refers to specialization of a subset of the template parameters in a multi-parameter template definition.

Let's summarize what we have so far:

/// General function template
template <typename POINT> inline
const Coord& getCoord(const POINT& p)
  {return p.coords;}

/// Partial specialization for pointers
/// to things
template <class POINT>
const Coord& getCoord(const POINT* p)
  {return p->coords;}

/// Complete specialization for Coord
inline
const Coord& getCoord(const Coord& p)
  {return p;}

/// Complete specialization for pointer
/// to Coord
inline
const Coord& getCoord(const Coord* p)
  {return *p;}

With those four getCoords put together, we have the following scenario:

If the element type of the container is anything but a Coord or Coord*, it will use the first or second definition of getCoord, depending on whether or not getCoord is called with a pointer to a POINT or a POINT itself;

Otherwise, it will use the appropriate complete specialization of getCoord, depending on whether or not getCoord is called with a pointer to a Coord or a Coord itself.

Our fitCurve() is now able to handle four cases of data sets:

Container<Coord>
Container<Coord*>
Container<Something>
Container<Something*>

The compiler can choose the right version of getCoord to use at compilation time. In the last two cases, as long as Something has a public data member called "coords", we are ok. Container can be any class that provides an iterator type (or whatever operations are required by the processor object or function).

The last generalization that we must do is to allow the "coords" to be a method instead of a data member. For instance,

class Point {
public:
  const Coord& coords() const
    {return coords_;}
private:
  Point coords_;
};

You probably know how to "point" to a method in a class. For instance, the "coords" method can be pointed to with a pointer of type "const Coord& (Point::*)() const". Given a typedef

typedef const Coord&
                (Point::* Method)() const;

This typedef defines a new type called Method, as a pointer to a const method of the Point class returning a reference to a const Coord. If this seems horribly difficult to read, don't worry, you're not the only one who feels that way. Pointers to functions and methods is one of the idiosyncrasies of C++. The syntax is atrociously difficult to get your mind around, but I guess it could be worse. In any case once you've done a few examples on your own it gets better. Here is an example of using a Method object:

Method mm = & Point::coords;
      // store pointer to coords method
Point point; // create a Point object
Coord coords = (point.*mm)();
      // #1: call coords method on it
Coord coords = point.coords();
      // #2: exact same thing

The line #2 does exactly the same thing as #1.

So the question is whether there is a way of doing the same thing with data members. Indeed, when getCoord accesses the coords field of the class, the compiler knows exactly what "coords" is: a data member or a method. So if we could write the general getCoord template like

template <class POINT>
const Coord& getCoord(const POINT& v) {
  return getData(v, &POINT::coords);
}

// partial specialization for pointers
template <class POINT>
const Coord& getCoord(const POINT* v) {
  return getData(*v, &POINT::coords);
}

and properly define two getData functions, one accepting a pointer to a method as second argument, and another accepting a pointer to a data member as second argument, we have accomplished our goal. The compiler will know which to choose without us having to tell it. In pseudo-language:

inline const Coord&
getData(const Point& pp, Method mm) {
  return (pp.*mm)();
}

inline const Coord&
getData(const Point& pp, ptr_dmem_Point dd) {
  return ...;
}

where Method is the typedef described earlier, ptr_dmem_Point stands for "pointer to data member of Point" and the ellipsis just means "don't know the syntax yet". It took me a bit of trial and error to find out the correct syntax, but it turns out it's not too bad: a "pointer" to a data member of type T for a class Point is "T Point::*". Simpler than defining a pointer to a method.

Our final solution for the getData is therefore, after replacing Point by a template parameter^[1]:

template <typename POINT>
inline const Coord&
getData(const POINT& pp, Coord POINT::* dd) {
  return pp.*dd;
}

template <typename POINT>
inline const Coord&
getData(const POINT& pp,
        const Coord& (POINT::* mm)() const) {
  return (pp.*mm)();
}

with the four function templates for getCoord mentioned above.

What does this give us?

Our fitCurve can use any container of Coord, Coord*, Something, or Something*, as long as the container has an "iterator" type defined in it, or whatever methods are required by fitCurve (!=, ++, etc).

"Something" must have a "coords" field, which must be either a Coord or a "const method returning a reference to a const Coord."

If we make any changes to our container type, no changes are needed to fitCurve, as long as the changes satisfy the minimal requirements of 1.

If we make any changes to the type of object stored in the container, no changes are needed to fitCurve, as long as the new object is something that satisfies 2. above;

The compiler, as it recompiles the class that uses fitCurve, will make use of the correct getCoord and getData without our intervention. This is probably the biggest gain.

Since everything is inlined, there are no function calls involved: everything is resolved at compile time and is equivalent to your having typed the coords data member straight where it is used by the processor object or function.

We now have a far more generic processor with only 15 lines of extra code, and one that requires almost NO intervention on our part when using the fitter with a new or different type of container and contained objects. Pretty good for 15 lines of code.

For a library developer, this level of generality may still be insufficient: the member in POINT must be called "coords". This is similar to STL containers which all have a member called "iterator" that defines an iterator appropriate for the container. To make it completely general, we would need a way of allowing the user to specify that they want something other than "coords" to be used by getCoord(). One work-around would be to define further complete specializations for your point class, using the appropriate member:

template <>
inline const Coord&
getCoord(const YourPoint& v) {
  return getData(v, &YourPoint::yourCoords);
}

and similarly for the pointer version. This is tedious to type and error-prone, but only a macro could be used to simplify this to a one-liner:

#define GET_COORD(YourPoint, yourData) \
template <> \
  inline const Coord& \
  getCoord(const YourPoint& v) { \
    return getData(v, &YourPoint::yourData);\
  } \
template <> \
  inline const Coord& \
  getCoord(const YourPoint* v) { \
    return getData(*v, &YourPoint::yourData);\
  }

which would allow you to type

GET_COORD(YourPointClass, yourCoordMember)

in your source file to get the specialization. The good news is that if you forget to define this, you get a compile time error. The bad news is that you have to define it in a place where it is visible to the compiler by the time your processor object or function calls getCoord, which is likely to increase the coupling between header files. The only other way that I can think of is to derive your class and provide a "coords" alias for the member, but this will be useful only if you have any control over the type of object stored in the container. For instance, you could derive YourPointClass as

struct PointDerived: YourPointClass {
  Coord& coords;
    // alias for member in YourPointClass
  PointDerived: coords(yourCoordMember) {}
};

and use a container of PointDerived objects instead of a container of YourPointClass objects. This only works if you have control over the element type of the container.

It is interesting to notice that templates are necessary in C++ only because C++ is such a strongly typed language. Consider Python, which is essentially untyped: classes are not differentiated by type, only by name. Hence a List class in Python that takes as argument the name of an object to store in the list, can have that object be any class of object. The idea of templates in Python is implicit in some ways, and unnecessary in others. There are probably many other languages where this applies. The strong-typing nature of C++ requires extra typing (sorry for pun), but it allows the compiler to know much more about the data being handled, and therefore to do much more stringent error-checking and optimizations not possible in weakly typed languages. Templates in C++ are necessary so C++ can support very useful features found in other high-level languages in a strongly-typed and optimized context.

Note: At the time of this writing, GNU g++ 3.0 (on SGI) has problems picking the correct getCoord: it seems to get confused by the pointer overloads. The code compiles and works perfectly, however, with SGI's MipsPro C++ compiler 7.3.1.

I showed how a processor (object or function) that uses data from a set of objects can be generalized with a very small number of lines of code, using templates and template specialization, to support application evolution, without requiring you to adapt the processor. More specifically, your processor object or function is able to extract the needed data from the container elements, regardless of whether the container element type.

Moreover, the compiler does so for you, automatically, without requiring your intervention. I'll gladly reply via email to suggestions and ideas. Sincere thanks to Phil Bass for his critical comments and ideas.

template <typename POINT> typedef
  const Coord& (POINT::* Method)() const;