function composition in C++ / C++11

Question

I am currently coding some cryptographic algorithms in C++11 that require a lot of function compositions. There are 2 types of composition I have to deal with :

1. Compose a function on itself a variable number of times. Mathematically, for a certain function F, F^n(x) = (F^{n-1} o F)(x) = F^{n-1}(F(x)).

2. Compose different functions together. For example, for some functions f,g,h,i,j and k of the same type, I'll have f(g(h(i(j(k(x)))))).

In my case, I'm using the following definition of F :

const std::vector<uint8_t> F(const std::vector<uint8_t> &x); 

I would like to compose this function on itself n times. I have implemented the composition in a simple recursive way which is working fine :

const std::vector<uint8_t> compose(const uint8_t n, const std::vector<uint8_t> &x) {     if(n > 1)        return compose(n-1, F(x));      return F(x); } 

For this case, is there a more efficient way an proper way to implement this composition using c++11 but without using BOOST ? It would be great to use this form if it is possible of course :

answer = compose<4>(F)(x); // Same as 'answer = F^4(x) = F(F(F(F(x))))' 

For the second case, I would like to implement the composition of a variable number of functions. For a given set of functions F0, F1, ..., Fn having the same definition as F, is there an efficient and proper way to compose them where n is variable ? I think variadic template would be useful here, but I don't know how to use them in that case.

Thanks for your help.

Answer 1

Something along these lines, perhaps (untested):

template <typename F> class Composer {   int n_;   F f_; public:   Composer(int n, F f) : n_(n), f_(f) {}    template <typename T>   T operator()(T x) const {     int n = n_;     while (n--) {       x = f_(x);     }     return x;   } };  template <int N, typename F> Composer<F> compose(F f) {   return Composer<F>(N, f); } 

EDIT: And for the second case (tested this time):

#include <iostream>  template <typename F0, typename... F> class Composer2 {     F0 f0_;     Composer2<F...> tail_; public:     Composer2(F0 f0, F... f) : f0_(f0), tail_(f...) {}      template <typename T>     T operator() (const T& x) const {         return f0_(tail_(x));     } };  template <typename F> class Composer2<F> {     F f_; public:     Composer2(F f) : f_(f) {}      template <typename T>     T operator() (const T& x) const {         return f_(x);     } };  template <typename... F> Composer2<F...> compose2(F... f) {     return Composer2<F...>(f...); }  int f(int x) { return x + 1; } int g(int x) { return x * 2; } int h(int x) { return x - 1; }  int main() {   std::cout << compose2(f, g, h)(42);   return 0; }