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Asked: 2026-05-30T16:41:54+00:00

I have a class hierarchy with the following three classes: template<int pdim > class

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I have a class hierarchy with the following three classes:

template<int pdim >
class Function
{
   virtual double operator()( const Point<pdim>& x) const = 0;
};

Which is a function in pdim-dimensional space, returning doubles.

template<int pdim, int ldim >
class NodeFunction
{
   virtual double operator()( const Node<pdim,ldim>& pnode, const Point<ldim>& xLoc) const = 0;
};

Which is a function from the ldim-dimensional local space of a node in pdim-dimensional space. 

template<int pdim, int ldim, int meshdim >
class PNodeFunction
{
   virtual double operator()( const PNode<pdim,ldim,meshdim>& pnode, const Point<ldim>& xLoc) const = 0;
};

Reason 1 for this design: a NodeFunction is more general than a Function. It can always map the local ldim-point point to a pdim-point. E.g an edge (Node with ldim=1) maps the interval [0,1] into pdim-dimensional physical space. That is why every Function is a NodeFunction. The NodeFunction is more general as the NodeFunction is allowed to query the Node for attributes.

Reason 2 for this design: a PNodeFunction is more general than a NodeFunction. Exactly one Node is accociated to every PNode (not vice versa). That is why every PNodeFunction is a NodeFunction. The PNodeFunction is more general as it also has all the context of the PNode which is part of a Mesh (thus it knows all its parents, neighbours, …).

Summary: Every Function<pdim> is a NodeFunction<pdim, ldim> for any parameter of ldim. Every NodeFunction<pdim, ldim> is a NodeFunction<pdim, ldim, meshdim> for any parameter of meshdim.

Question: What is the best way to express this in C++, such that I can use Function in place of NodeFunction / PNodeFunction, such that the code is fast (it is a high performance computing code), such that the Code works for

The template parameters are not completely independent but rather dependend on each other:
– pdim=1,2,3 (main interest) but it is nice if it works also for values of pdim up to 7.
– ‘ldim=0,1,…,pdim’
– ‘meshdim=ldim,ldim+1,…,pdim’

To consider the performance, note that obly a few functions are created in the program, but their operator() is called many times.

Variants

I thought about a few ways to implement this (I currently implemented Variant 1). I wrote it down here so that you can tell me about the advanage and disadvantage of these approaches.

Variant 1

Implement the above described inheritance A<dim> inherits from B<dim,dim2> via a helper template Arec<dim,dim2>. In pseudo Code this is

class A<dim> : public Arec<dim,dim>;
class Arec<dim,dim2> : public Arec<dim,dim2-1>, public B<dim,dim2>;
class Arec<dim,0> : public B<dim,dim2>;

This is applied both to inherit Function from NodeFunction and NodeFunction from PNodeFunction. As NodeFunction inherits roughly O(pdim^2) times from PNodeFunction how does this scale? Is this huge virtual table bad?

Note: In fact every Function should also inherit from VerboseObject, which allows me to print debugging information about the function to e.g. std::cout. I do this by virtually inheritung PNodeFunction from VerboseObject. How will this impact the performance? This should increase the time to construct a Function and to print the debug information, but not the time for operator(), right?

Variant 2

Don’t express the inheritance in C++, e.g. A<dim> doesn inherit from B<dim,dim2> bur rather there is a function to convert the two

class AHolder<dim,dim2> : public B<dim, dim> {

}

std::shared_pointer< AHolder<dim,dim2> > interpretAasB( std::shared_pointer< AHolder<dim> >)
 [...]

This has the disadvanate that I can no longer use Function<dim> in place of NodeFunction<dim> or PNodeFunction<dim>.

Variant 3

What is your prefered way to implement this?

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1 Answer

  1. Editorial Team

    I don’t comprehend you problem very well; that might be because I lack specific knowledge of the problem domain.

    Anyway it seems like you want to generate a hierarchy of classes, with Function (most derived class) at the bottom, and PNodeFunction at the top (least derived class).
    For that I can only recommend Alexandrescu’s Modern C++ design book, especially the chapter on hierarchy generators.
    There is an open source library stemming from the book called Loki.
    Here’s the part that might interest you.

    Going the generic meta-programming way might be the hardest but I think it will result in ease of use once setup, and possibly increased performance (that is always to be verified by the profiler) compared to virtual inheritance.

    In any case I strongly recommend not inheriting from the Verbose object for logging, but rather having a separate singleton logging class.
    That way you don’t need the extra space in the class hierarchy to store a logging object.
    You could have only the least derived class inherit from the Verbose object but your function classes are not logging objects; they use a logging object (I may be a bit pedantic here).
    The other problem is if you inherit multiple times from that base class, you’ll end up with multiple copies of the logging object and have to use virtual inheritance to solve it.

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