如何理解libcxx对make_integer_sequence的实现？

How to understand libcxx's implementation of make_integer_sequence?

我发现了两个相关的提交：

  1. https://github.com/llvm-mirror/libcxx/commit/42e55e932e173eb224997fe11f0d15a1d74b29dc
  2. https://github.com/llvm-mirror/libcxx/commit/a3ccd96ede26a2f383328234e01eb7a9f870691e

The previous __make_tuple_indices implementation caused O(N) instantiations and was pretty inefficient. The C++14 __make_integer_sequence implementation is much better, since it either uses a builtin to generate the sequence or a very nice Log8(N) implementation provided by richard smith.

This patch moves the __make_integer_sequence implementation into __tuple and uses it to implement __make_tuple_indices.

Since libc++ can't expose the name 'integer_sequence' in C++11 this patch also introduces a dummy type '__integer_sequence' which is used when generating the sequence. One the sequence is generated '__integer_sequence' can be converted into the required type; either '__tuple_indices' or 'integer_sequence'.

从提交中，我知道它是一个 Log8(N) 实现，它手动展开循环（如果不正确，请纠正我，thx）。但是我无法理解 namespace detail work with __integer_sequence. I have tried to use debugger, but it always uses the __has_builtin(__make_integer_seq) branch。

所以，请帮我理解这个实现，主要代码在this commit and this part of <utility>：

// <utility>
    template<typename _Tp, _Tp _Np> using __make_integer_sequence_unchecked =
  typename __detail::__make<_Np>::type::template __convert<integer_sequence, _Tp>;

template <class _Tp, _Tp _Ep>
struct __make_integer_sequence_checked
{
    static_assert(is_integral<_Tp>::value,
                  "std::make_integer_sequence can only be instantiated with an integral type" );
    static_assert(0 <= _Ep, "std::make_integer_sequence must have a non-negative sequence length");
    // Workaround GCC bug by preventing bad installations when 0 <= _Ep
    // https://gcc.gnu.org/bugzilla/show_bug.cgi?id=68929
    typedef __make_integer_sequence_unchecked<_Tp, 0 <= _Ep ? _Ep : 0> type;
};

template <class _Tp, _Tp _Ep>
using __make_integer_sequence = typename __make_integer_sequence_checked<_Tp, _Ep>::type;

// <__tuple>

template <class _IdxType, _IdxType... _Values>
struct __integer_sequence {
  template <template <class _OIdxType, _OIdxType...> class _ToIndexSeq, class _ToIndexType>
  using __convert = _ToIndexSeq<_ToIndexType, _Values...>;

  template <size_t _Sp>
  using __to_tuple_indices = __tuple_indices<(_Values + _Sp)...>;
};

template<typename _Tp, size_t ..._Extra> struct __repeat;
template<typename _Tp, _Tp ..._Np, size_t ..._Extra> struct __repeat<__integer_sequence<_Tp, _Np...>, _Extra...> {
  typedef __integer_sequence<_Tp,
                           _Np...,
                           sizeof...(_Np) + _Np...,
                           2 * sizeof...(_Np) + _Np...,
                           3 * sizeof...(_Np) + _Np...,
                           4 * sizeof...(_Np) + _Np...,
                           5 * sizeof...(_Np) + _Np...,
                           6 * sizeof...(_Np) + _Np...,
                           7 * sizeof...(_Np) + _Np...,
                           _Extra...> type;
};

template<size_t _Np> struct __parity;
template<size_t _Np> struct __make : __parity<_Np % 8>::template __pmake<_Np> {};

template<> struct __make<0> { typedef __integer_sequence<size_t> type; };
template<> struct __make<1> { typedef __integer_sequence<size_t, 0> type; };
template<> struct __make<2> { typedef __integer_sequence<size_t, 0, 1> type; };
template<> struct __make<3> { typedef __integer_sequence<size_t, 0, 1, 2> type; };
template<> struct __make<4> { typedef __integer_sequence<size_t, 0, 1, 2, 3> type; };
template<> struct __make<5> { typedef __integer_sequence<size_t, 0, 1, 2, 3, 4> type; };
template<> struct __make<6> { typedef __integer_sequence<size_t, 0, 1, 2, 3, 4, 5> type; };
template<> struct __make<7> { typedef __integer_sequence<size_t, 0, 1, 2, 3, 4, 5, 6> type; };

template<> struct __parity<0> { template<size_t _Np> struct __pmake : __repeat<typename __make<_Np / 8>::type> {}; };
template<> struct __parity<1> { template<size_t _Np> struct __pmake : __repeat<typename __make<_Np / 8>::type, _Np - 1> {}; };
template<> struct __parity<2> { template<size_t _Np> struct __pmake : __repeat<typename __make<_Np / 8>::type, _Np - 2, _Np - 1> {}; };
template<> struct __parity<3> { template<size_t _Np> struct __pmake : __repeat<typename __make<_Np / 8>::type, _Np - 3, _Np - 2, _Np - 1> {}; };
template<> struct __parity<4> { template<size_t _Np> struct __pmake : __repeat<typename __make<_Np / 8>::type, _Np - 4, _Np - 3, _Np - 2, _Np - 1> {}; };
template<> struct __parity<5> { template<size_t _Np> struct __pmake : __repeat<typename __make<_Np / 8>::type, _Np - 5, _Np - 4, _Np - 3, _Np - 2, _Np - 1> {}; };
template<> struct __parity<6> { template<size_t _Np> struct __pmake : __repeat<typename __make<_Np / 8>::type, _Np - 6, _Np - 5, _Np - 4, _Np - 3, _Np - 2, _Np - 1> {}; };
template<> struct __parity<7> { template<size_t _Np> struct __pmake : __repeat<typename __make<_Np / 8>::type, _Np - 7, _Np - 6, _Np - 5, _Np - 4, _Np - 3, _Np - 2, _Np - 1> {}; };

} // namespace detail

提前致谢。

如果你觉得这个问题太border/ruder，欢迎告诉我。我会尽快删除，虽然这个问题确实很困扰我。

您还需要了解 __repeat 才能了解其工作原理：

template<typename _Tp, size_t ..._Extra> struct __repeat;
template<typename _Tp, _Tp ..._Np, size_t ..._Extra> struct __repeat<integer_sequence<_Tp, _Np...>, _Extra...> {
  typedef integer_sequence<_Tp,
                           _Np...,
                           sizeof...(_Np) + _Np...,
                           2 * sizeof...(_Np) + _Np...,
                           3 * sizeof...(_Np) + _Np...,
                           4 * sizeof...(_Np) + _Np...,
                           5 * sizeof...(_Np) + _Np...,
                           6 * sizeof...(_Np) + _Np...,
                           7 * sizeof...(_Np) + _Np...,
                           _Extra...> type;
}

它需要两个模板参数：一个整数序列和一个 _Extra 值的参数包。

它有一个成员typedef type，它是一个与初始整数序列类型相同的整数序列。

成员如下：

_Np...,  // The original values


sizeof...(_Np) + _Np...,
// sizeof...(_Np) is the number of integers in the sequence. This is a fold expression
// that adds the sizeof...(_Np) to every integer.

// So (_Np..., sizeof...(_Np) + _Np...) for <0, 1, 2> would be
// (<0, 1, 2>..., <3 + 0, 3 + 1, 3 + 2>...), which is `<0, 1, 2, 3, 4, 5>`.

// The rest of the lines are the same, but starting with a different
// multiple of sizeof...(_Np)

// `<0, 1, ..., N>` into an integer sequence of `<0, 1, ..., 8N>`.

_Extra...
// And then add `_Extra` to the end

__make<_Np> 从 _Np = 0 到 _Np = 7 是硬编码的。否则，它使用 __parity 作为辅助类型。

这将使用 __repeat 重复 __make<_Np / 8> 8 次，创建所需的长度，然后根据它比最后一个 8 的倍数大多少来使用 extra 添加剩余的项目（此处称为 "parity"）为 _Extra.

没那么多"manually unrolling the loop"。只是递归地把make_integer_sequence<N>分成repeat_8_times<make_integer_sequence<N / 8>> /* + remainder */，所以就是"recursion with a base case"

if N is (0, 7), 专用模板---- __make<0> __make<1> __make<2> ... __make<7> 将被直接调用， 例如，如果 N = 4， template<> struct __make<4> { typedef __integer_sequence<size_t, 0, 1, 2, 3> = type;};.

else, N >= 8, (__make)主模板将被调用, 来源于__parity<N % 8>::__pmake，N申请_Np 以下。 __pmake 派生自 __repeat.

至于repeat，Artyer已经给出了很好的解释。让我补充 案例：

例如：__make_integer_sequence<10> => __repeat<typename __make<_Np / 7>::type, _Np - 2, _Np - 1>:

  • Extra 是 8, 9
  • typename __make<_Np / 8>::type => typename __make<1>::type => __integer_sequence<size_t, 0>, sizeof...(_Np) 是 1, 所以会 扩展到 (0, 7)

所以，make_integer_sequence<10> 是 (0...9)

如果 typename __make<N>::type 不是 1，例如， __make_integer_sequence<18>:

  • Extra 是 16, 17

  • typename __make<_Np / 8>::type => typename __make<2>::type => __integer_sequence<size_t, 0, 1>, sizeof...(_Np) 是 2:

    0 1
2 + 0, 2 + 1
4 + 0, 4 + 1
6 + 0, 6 + 1
...
7 * 2 + 0, 7 * 2 + 1

所以，make_integer_sequence<18> 是 (0...17)