For the life of me, I can't get this simple piece of arcane template magic to work:
template<typename T, int a, int b>
int f(T v){
  return v*a-b; // just do something for example
}
template<typename T, int a, int b, template<typename,int,int> class func>
class C{
  int f(){
    return func<T,a,b>(3);
  }
};
int main(){
  C<float,3,2, f> c;
}
Is this possible to do without involving functors?
f is supposed to be a class - you have a function.
See below:
// Class acts like a function - also known as functor.
template<typename T, int a, int b>
class f
{
  int operator()(T v)
  {
    return v*a-b; // just do something for example
  }
};
template<typename T, int a, int b, template<typename,int,int> class func>
class C
{
  int f()
  {
    return func<T,a,b>(3);
  }
};
int main()
{
  C<float,3,2, f> c;
}
... And the adapted version if you need to port legacy code (Adapts the function to a class template):
#include <iostream>
template<typename T, int a, int b>
int f(T v)
{
  std::cout << "Called" << std::endl;
  return v*a-b; // just do something for example
}
template<typename T, int a, int b, template<typename,int,int> class func>
struct C
{
  int f()
  {
    return func<T,a,b>(3);
  }
};
template <class T, int a, int b>
struct FuncAdapt
{
  T x_;
  template <class U>
  FuncAdapt( U x )
  : x_( x )
  {}
  operator int() const
  {
    return f<T,a,b>( x_ );
  }
};
int main()
{
  C<float,3,2, FuncAdapt > c;
  c.f();
}
                        You can solve it through a little trickery:
template<typename T, int a, int b>
int f(T v){
  return v*a-b; // just do something for example
}
template<typename T, int, int>
using func_t = int (*)(T);
template<typename T, int a, int b, func_t<T, a, b> func>
class C{
  int f(){
    return func(3);
  }
};
C<float,3,2, f<float, 3, 2>> c;
First you need a type-alias for the function (func_t above), and you unfortunately need to duplicate the template arguments in the declaration of c.
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