#pragma once

#include <array>
#include <cmath>

template <typename T, std::size_t N>
struct signal : public std::array<T, N>
{

  constexpr signal() {}

  constexpr signal(T begin, T end)
  {
    static_assert(N > 1, "N must be bigger than 1");	  
    float step = (end - begin) / (N - 1);

    for (std::size_t i = 0; i < N; i++)
    {
      this->at(i) = begin + i * step;
    }
  }

  constexpr signal(const std::array<T, N> &x, auto fun)
  {
    for (std::size_t i = 0; i < N; i++)
    {
      this->at(i) = fun(x.at(i));
    }
  }

  constexpr signal(const signal &sig, auto fun)
  {
    for (std::size_t i = 0; i < N; i++)
    {
      this->at(i) = fun(sig.at(i));
    }
  }

  constexpr signal operator+(const T &t) const
  {
    return signal(*this, [&](T elem)
                  { return elem + t; });
  };

  constexpr signal operator-(const T &t) const
  {
    return signal(*this, [&](T elem)
                  { return elem - t; });
  };

  constexpr signal operator*(const T &t) const
  {
    return signal(*this, [&](T elem)
                  { return elem * t; });
  };

  constexpr signal operator/(const T &t) const
  {
    return signal(*this, [&](T elem)
                  { return elem / t; });
  };

  constexpr signal operator+(const signal &sig) const
  {
    signal ret;
    for (std::size_t i = 0; i < N; i++)
    {
      ret.at(i) = this->at(i) + sig.at(i);
    }
    return ret;
  };

  constexpr signal operator-(const signal &sig) const
  {
    signal ret;
    for (std::size_t i = 0; i < N; i++)
    {
      ret.at(i) = this->at(i) - sig.at(i);
    }
    return ret;
  };

  friend constexpr signal operator+(const T &t, const signal &sig)
  {
    return sig + t;
  }

  friend constexpr signal operator*(const T &t, const signal &sig)
  {
    return sig * t;
  }

  friend constexpr signal operator/(const T &t, const signal &sig)
  {
    signal ret;
    for (std::size_t i = 0; i < N; i++)
    {
      ret.at(i) = t / sig.at(i);
    }
    return ret;
  }
};