Compile time recursive objects in C++

The article explores the possibilities of generic programming offered by the template features of C++. We define compile time recursive objects as instances of class templates which contain other instances of the same template as member variables. With such templates we can define containers that contain objects of arbitrary types, but where the type of each element is known at compile time. The structure of the container is therefore fixed. The technique mimics the polymorphism achieved with dynamic binding and inheritance using static binding and template specialisation. It is obviously less flexible but offers considerable performance gains at runtime. We give the template definitions for compile time recursive lists and explain how to perform operations on these lists. As an example application, we use compile time lists in the definition of templates for special sparse vectors and matrices. In these vectors and matrices, the sparseness pattern can be arbitrary but must be known at compile time. The tracking of zero and nonzero elements is performed at compile time. This allows the programmer to use abstract vector and matrix expressions and still reach performance equal to hand coded operations. This is possible since the compiler can locate the elementary expressions between zero entries and discard them entirely from the resulting code