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# A look at compile time computation in C++
The C++ language landscape may be pretty old by now but that doesn't mean that its continental plates have ceased their movement and no new and exciting things happen anymore. To the contrary the recently approved _C++14_ standard continues in the footsteps of _C++11_ by continuing to modernize and empower the language by e.g. introducing _generic lambda expressions_ and relaxing the restrictions on the `constexpr` keyword introduced by _C++11_ back in 2011. Especially the last improvement caused me to think about how one could use the new language features to perform compile time computation in a fashion actually applicable in practice. This is what I want to talk about in this article.
Besides C-style macros C++ templates present one additional language element that is guaranteed by the standard to be executed at compile time. In this context the [proof] that this template system is Turing complete manages to both illustrate its power and demonstrate its bewildering complexity. As it is pretty unrealistic that one would implement _common application logic_ in terms of a Turing machine just to achieve compile time computation, a easier way of expressing _compile time programs_ has to be found.
## Compile time list processing
My first attempt at facilitating compile time computation is a _functional-style_ list library based on template metaprogramming: [ConstList]. This library handles lists in a fashion simmilar to how it is done in languages such as Scheme or Haskell, i.e. by providing functions such as `fold` and `map` which manipulate a basic list type based on _Cons_ expressions. As an example one may consider how ConstList's `map` function is expressed in terms of `foldr`:
~~~
template <
typename Cons,
typename Function
>
constexpr auto map(const Cons& cons, const Function& function) {
return foldr(
cons,
[&function](auto car, auto cdr) {
return concatenate(make(function(car)), cdr);
},
make()
);
}
~~~
{: .language-cpp}
The `foldr` implementation is also quite straightforward and simply applies a given function to each pair of the _Cons_ structure using static recursion. Note that this approach of _lambda expression based_ template metaprogramming would have been much more verbose in C++11 as many list manipulators such as `map` and `foldr` make use of C++14's _generic lambda expressions_. While the [test cases] provide a set of - in my opinion - reasonably nice list transformations and queries they also present the core problem of the particular approach taken in ConstList, as it is impossible to return lists of varying lengths depending on their contents. This pervasive limitation exists because the only way to vary types at compile time depending on values is to use these values as template parameters. That is the _Cons_ list type tree would have to be both list declaration and definition, analogously to e.g. `std::integral_constant`. Obviously this is quite different from how types and values were separated into templates and member constants in ConstList. One would have to think of types as values and templates as functions that modify those values instead.
To summarize: The approach taken in my implementation of ConstList may be a nice exercise in template metaprogramming and writing functional style C++ code but its practical applications in compile time computation are unreasonably narrow.
## Types as values…
…and templates as functions.
## Spectroscopy of `constexpr`
As was already mentioned, prior to the C++11 standard the only way to perform compile time computations was to rely on macros and template metaprogramming. While both of those can be thought of as separate functional-style languages inside C++, the `constexpr` keyword allows one to declare a normal function as _potentially executable_ at compile time. So contrary to template metaprogramming based solutions we don't have a strong guarantee that our _compile time program_ is actually evaluated at compile time and would have to look at the generated Assembler output when in doubt. Sadly this is actually not much more than what is possible in _normal_ C++ compiled by a _sufficiently smart compiler_, e.g. the listing below is evaluated at compile time by gcc without any usage of `constexpr` or template metaprogramming:
~~~
int example(int x) {
return 2 * x;
}
int recursive_example(const int& target, int current = 0) {
if ( current == target) {
return current;
} else {
return recursive_example(target, ++current);
}
}
int main(int, char**) {
return example(
recursive_example(21)
);
}
~~~
{: .language-cpp}
Where the verbose Assembler output is aquired as follows (note that the same command also works for Clang):
~~~
> g++ -S -fverbose-asm -O2 example.cc -o example.asm
> grep example.asm -n -e 42
95: movl $42, %eax #,
~~~
{: .language-sh}
[proof]: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.3670
[ConstList]: /page/const_list/
[test cases]: https://github.com/KnairdA/ConstList/blob/master/test.cc
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