c++ - 在编译时使用 C++17 可变模板遍历树

Question

我目前正在研究使用 C++ (C++17) 可变参数模板来生成高效、实时的电路仿真。
我的目标是利用可变参数模板来定义可以在编译时遍历的树。为了定义这样的树，我使用了以下三个结构:

template <auto Tag> struct Leaf
{
    static constexpr auto tag = Tag;
};

template <typename ... Children> struct Branch
{
    static constexpr auto child_count = sizeof ... (Children);
    
    template <typename Lambda> constexpr void for_each_child(Lambda && lambda)
    {
        // TODO: Execute 'lambda' on each child.
    }
    
    std::tuple<Children ...> m_children {};
};

template <typename Root> struct Tree
{
    template <auto Tag> constexpr auto & get_leaf()
    {
        // TODO: Traverse the tree and find the leaf with tag 'Tag'.
        
        // If there's no leaf with tag 'Tag' the program shouldn't compile.
    }
    
    Root root {};
};

使用上面的树的定义，我们可以定义一组电路组件如下:

template <auto Tag> struct Resistor : Leaf<Tag>
{
    float resistance() { return m_resistance; }
    
    float m_resistance {};
};

template <auto Tag> struct Capacitor : Leaf<Tag>
{
    float resistance() { return 0.0f; }
    
    float m_capacitance {};
};

template <typename ... Children> struct Series : Branch<Children ...>
{
    using Branch<Children ...>::for_each_child;
    
    float resistance()
    {
        float acc = 0.0f;
        
        for_each_child([&acc](auto child) { acc += child.resistance(); });
        
        return acc;
    }
};

template <typename ... Children> struct Parallel : Branch<Children ...>
{
    using Branch<Children ...>::for_each_child;
    
    float resistance()
    {
        float acc = 0.0f;
        
        for_each_child([&acc](auto child) { acc += 1.0f / child.resistance(); });
        
        return 1.0f / acc;
    }
};

接下来，利用上面的组件，我们可以这样表达一个具体的电路:

enum { R0, R1, C0, C1 };

using Circuit =
    Tree<
        Parallel<
            Series<
                Resistor<R0>,
                Capacitor<C0>
            >, // Series
            Series<
                Resistor<R0>,
                Capacitor<C1>
            > // Series
        > // Parallel
    >; // Tree

...其中 R0、R1、C0 和 C1 是我们在编译时用于访问组件的标记。例如。一个非常基本的用例可能如下:

int main()
{
    Circuit circuit {};
    
    circuit.get_leaf<R0>().m_resistance  =  5.0E+3f;
    circuit.get_leaf<C0>().m_capacitance = 10.0E-3f;
    circuit.get_leaf<R1>().m_resistance  =  5.0E+6f;
    circuit.get_leaf<C1>().m_capacitance = 10.0E-6f;
    
    std::cout << circuit.root.resistance() << std::endl;
}

我无法理解的是如何实现 for_each_child 和 get_leaf 函数。我尝试过使用 if-constexpr 语句和模板结构的不同方法，但没有找到好的解决方案。可变参数模板很有趣，但同时也令人生畏。任何帮助将不胜感激。

Answer 1

for_each_child 与 std::index_sequence 相当简单。

template <typename ... Children> struct Branch
{
    using indexes = std::index_sequence_for<Children...>;
    static constexpr auto child_count = sizeof... (Children);
    
    template <typename Lambda> constexpr void for_each_child(Lambda && lambda)
    {
        for_each_child_impl(std::forward<Lambda>(lambda), indexes{});
    }
    
    std::tuple<Children ...> m_children {};

private:
    template <typename Lambda, std::size_t... Is> constexpr void for_each_child_impl(Lambda && lambda, std::index_sequence<Is...>)
    {
        (lambda(std::get<Is>(m_children)), ...);
    }
};

get_leaf 稍微有点棘手。首先，我们确定到达所需叶子的路径是什么，然后我们遵循 root 的路径。

template <std::size_t I, typename>
struct index_sequence_cat;

template <std::size_t I, std::size_t... Is>
struct index_sequence_cat<I, std::index_sequence<Is...>> {
    using type = std::index_sequence<I, Is...>;
};

template <std::size_t I, typename Ix>
using index_sequence_cat_t = typename index_sequence_cat<I, Ix>::type;

template<typename, auto Tag, typename, std::size_t... Is> 
struct leaf_index {};

template<auto Tag, typename T, std::size_t... Is> 
using leaf_index_i = typename leaf_index<void, Tag, T, Is...>::index;

template<auto Tag, std::size_t I> 
struct leaf_index<void, Tag, Leaf<Tag>, I> {
    using index = std::index_sequence<I>;
};

template<typename, auto, std::size_t, typename...>
struct branch_index {};

template<auto Tag, std::size_t I, typename... Args>
using branch_index_i = typename branch_index<void, Tag, I, Args...>::index;

template<auto Tag, std::size_t I, typename First, typename... Args>
struct branch_index<std::void_t<leaf_index_i<Tag, First, I>>, Tag, I, First, Args...> {
    using index = leaf_index_i<Tag, First, I>;
};

template<auto Tag, std::size_t I, typename First, typename... Args>
struct branch_index<std::void_t<branch_index_i<Tag, I + 1, Args...>>, Tag, I, First, Args...> {
    using index = branch_index_i<Tag, I + 1, Args...>;
};

template<auto Tag, typename... Children, std::size_t I> 
struct leaf_index<void, Tag, Branch<Children...>, I> {
    using index = index_sequence_cat_t<I, branch_index_i<Tag, 0, Children...>>;
};

template<auto Tag, typename... Children> 
struct leaf_index<std::void_t<branch_index_i<Tag, 0, Children...>>, Tag, Branch<Children...>> {
    using index = branch_index_i<Tag, 0, Children...>;
};

template <typename Root> struct Tree
{
    template <auto Tag> constexpr auto & get_leaf()
    {
        return get_leaf(leaf_index<Tag, root>{});
    }
    
    Root root {};
private:
    template <std::size_t... Is>
    auto & get_leaf(std::index_sequence<Is...>)
    {
        return get_leaf<Is...>(root);
    }

    template<std::size_t I, typename T>
    auto& get_leaf(T & branch)
    {
        return std::get<I>(branch.m_children);
    }
    
    template<std::size_t I, std::size_t J, std::size_t... Is, typename T>
    auto& get_leaf(T & branch)
    {
        return get_leaf<J, Is...>(std::get<I>(branch.m_children));
    }
};