17.5 Computational Completeness
The Pow<> and Sqrt<> examples show that a template metaprogram can contain:
State variables: the template parameters
Loop constructs: through recursion
Path selection: by using conditional expressions or specializations
If there are no limits to the amount of recursive instantiations and the amount of state variables that are allowed, it can be shown that this is sufficient to compute anything that is computable. However, it may not be convenient to do so using templates. Furthermore, template instantiation typically requires substantial compiler resources, and extensive recursive instantiation quickly slows down a compiler or even exhausts the resources available. The C++ standard recommends but does not mandate that 17 levels of recursive instantiations be allowed as a minimum. Intensive template metaprogramming easily exhausts such a limit.
Hence, in practice, template metaprograms should be used sparingly. The are a few situations, however, when they are irreplaceable as a tool to implement convenient templates. In particular, they can sometimes be hidden in the innards of more conventional templates to squeeze more performance out of critical algorithm implementations.