C++ 基于另一个可变参数包查找可变数据包的收缩_C++_C++11_Multidimensional Array_Template Meta Programming

C++ 基于另一个可变参数包查找可变数据包的收缩

c++ c++11

C++ 基于另一个可变参数包查找可变数据包的收缩,c++,c++11,multidimensional-array,template-meta-programming,C++,C++11,Multidimensional Array,Template Meta Programming,我正在研究一个静态多维数组压缩框架，我遇到了一个有点难以解释的问题，但我会尽我所能。假设我们有一个N维数组类 template<typename T, int ... dims> class Array {} 我现在有一个函数construction，它的签名应该如下所示 template<T, int ... Dims, int ... Idx, typename std::enable_if<sizeof...(Dims)==sizeof...(Idx),bool

我正在研究一个静态多维数组压缩框架，我遇到了一个有点难以解释的问题，但我会尽我所能。假设我们有一个

维数组类

template<typename T, int ... dims>
class Array {}

我现在有一个函数

construction

，它的签名应该如下所示

template<T, int ... Dims, int ... Idx, 
typename std::enable_if<sizeof...(Dims)==sizeof...(Idx),bool>::type=0>
Array<T,apply_to_dims<Dims...,do_contract<Idx...>>> 
contraction(const Indices<Idx...> &idx, const Array<T,Dims...> &a)

因此，本质上，给定

Idx…

和

Dims…

两者大小相同，检查

Idx…

中的哪些值相等，获取它们出现的位置，并删除

Dims…

中的相应条目（位置）。这本质上是一个问题

数组收缩规则：

索引的参数数量和数组的维度/秩应该相同，即

sizeof…（Idx）==sizeof…（Dims）

Idx

和

dim

之间存在一对一的对应关系，即如果我们有

索引

和

数组

，

映射到

，

映射到

和

映射到

如果

Idx

中存在相同/相等的值，则意味着收缩，这意味着

Dims

中的相应维度应该消失，例如，如果我们有

索引

和

数组

，然后

0==0

以及这些值映射到的

和

的相应维度都需要消失，结果数组应该是

array

如果

Idx

具有相同的值，但相应的

Dims

不匹配，则应触发编译时错误，例如，

索引

和

数组

，因为

4=5

，同样的

索引

也不可能像

4=6

，这将导致

不同维度的数组不可能收缩，例如，

Array

不能以任何方式收缩

只要相应的

Dims

也匹配，则

Idx允许多对、三元组、四元组等，例如索引将收缩为数组，前提是输入数组为数组


我对元编程的了解并没有达到实现此功能的程度，但我希望我已经明确了意图，以便有人能引导我朝着正确的方向前进。
这是一个混乱，但我认为它做了您希望它做的事情。几乎可以肯定的是，可以对此进行许多简化，但这是我第一次通过测试。请注意，这并没有实现收缩，只是确定了应该是什么类型。如果这不是你需要的，我提前道歉
#include <type_traits>

template <std::size_t...>
struct Indices {};

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

// Count number of 'i' in 'rest...', base case
template <std::size_t i, std::size_t... rest>
struct Count : std::integral_constant<std::size_t, 0>
{};

// Count number of 'i' in 'rest...', inductive case
template <std::size_t i, std::size_t j, std::size_t... rest>
struct Count<i, j, rest...> :
    std::integral_constant<std::size_t,
                           Count<i, rest...>::value + ((i == j) ? 1 : 0)>
{};

// Is 'i' contained in 'rest...'?
template <std::size_t i, std::size_t... rest>
struct Contains :
    std::integral_constant<bool, (Count<i, rest...>::value > 0)>
{};


// Accumulation of counts of indices in all, base case
template <typename All, typename Remainder,
          typename AccIdx, typename AccCount>
struct Counts {
    using indices = AccIdx;
    using counts = AccCount;
};

// Accumulation of counts of indices in all, inductive case
template <std::size_t... all, std::size_t i, std::size_t... rest,
          std::size_t... indices, std::size_t... counts>
struct Counts<Indices<all...>, Indices<i, rest...>,
              Indices<indices...>, Indices<counts...>>
    : std::conditional<Contains<i, indices...>::value,
                       Counts<Indices<all...>, Indices<rest...>,
                              Indices<indices...>,
                              Indices<counts...>>,
                       Counts<Indices<all...>, Indices<rest...>,
                              Indices<indices..., i>,
                              Indices<counts...,
                                      Count<i, all...>::value>>>::type
{};

// Get value in From that matched the first value of Idx that matched idx
template <std::size_t idx, typename Idx, typename From>
struct First : std::integral_constant<std::size_t, 0>
{};
template <std::size_t i, std::size_t j, std::size_t k,
          std::size_t... indices, std::size_t... values>
struct First<i, Indices<j, indices...>, Indices<k, values...>>
    : std::conditional<i == j,
                       std::integral_constant<std::size_t, k>,
                       First<i, Indices<indices...>,
                             Indices<values...>>>::type
{};

// Return whether all values in From that match Idx being idx are tgt
template <std::size_t idx, std::size_t tgt, typename Idx, typename From>
struct AllMatchTarget : std::true_type
{};
template <std::size_t idx, std::size_t tgt,
          std::size_t i, std::size_t j,
          std::size_t... indices, std::size_t... values>
struct AllMatchTarget<idx, tgt,
                      Indices<i, indices...>, Indices<j, values...>>
    : std::conditional<i == idx && j != tgt, std::false_type,
                       AllMatchTarget<idx, tgt, Indices<indices...>,
                                      Indices<values...>>>::type
{};

/* Generate the dimensions, given the counts, indices, and values */
template <typename Counts, typename Indices,
          typename AllIndices, typename Values, typename Accum>
struct GenDims;

template <typename A, typename V, typename R>
struct GenDims<Indices<>, Indices<>, A, V, R> {
    using type = R;
};
template <typename T, std::size_t i, std::size_t c,
          std::size_t... counts, std::size_t... indices,
          std::size_t... dims, typename AllIndices, typename Values>
struct GenDims<Indices<c, counts...>, Indices<i, indices...>,
               AllIndices, Values, Array<T, dims...>>
{
    static constexpr auto value = First<i, AllIndices, Values>::value;
    static_assert(AllMatchTarget<i, value, AllIndices, Values>::value,
                  "Index doesn't correspond to matching dimensions");
    using type = typename GenDims<
        Indices<counts...>, Indices<indices...>,
        AllIndices, Values,
        typename std::conditional<c == 1,
                                  Array<T, dims..., value>,
                                  Array<T, dims...>>::type>::type;
};

/* Put it all together */
template <typename I, typename A>
struct ContractionType;

template <typename T, std::size_t... indices, std::size_t... values>
struct ContractionType<Indices<indices...>, Array<T, values...>> {
    static_assert(sizeof...(indices) == sizeof...(values),
                   "Number of indices and dimensions do not match");
    using counts = Counts<Indices<indices...>,
                          Indices<indices...>,
                          Indices<>, Indices<>>;
    using type = typename GenDims<typename counts::counts,
                                  typename counts::indices,
                                  Indices<indices...>, Indices<values...>,
                                  Array<T>>::type;
};

static_assert(std::is_same<typename
              ContractionType<Indices<0, 0>, Array<double, 3, 3>>::type,
              Array<double>>::value, "");
static_assert(std::is_same<typename
              ContractionType<Indices<0, 1>, Array<double, 3, 3>>::type,
              Array<double, 3, 3>>::value, "");
static_assert(std::is_same<typename
              ContractionType<Indices<0, 1, 0>, Array<double, 3, 4, 3>>::type,
              Array<double, 4>>::value, "");
static_assert(std::is_same<typename
              ContractionType<Indices<0, 1, 0, 7, 7, 2>,
              Array<double, 3, 4, 3, 5, 5, 6>>::type,
              Array<double, 4, 6>>::value, "");

// Errors appropriately when uncommented
/* static_assert(std::is_same<typename */
/*               ContractionType<Indices<10,10, 2, 3>, */
/*               Array<double, 5,6,4,4>>::type, */
/*               Array<double>::value, ""); */

#包括
样板
结构索引{}；
样板
结构数组{}；
//在“rest…”中计算“i”的数目，基本情况
样板
结构计数：标准：：整型常量
{};
//计数“rest…”中的“i”个数，归纳情况
样板
结构计数：
积分常数
{};
//“我”是否包含在“休息…”中？
样板
结构包含：
标准：积分（常数0）>
{};
//所有基本情况下的指数计数累积
样板
结构计数{
使用指数=AccIdx；
使用计数=AccCount；
};
//在所有归纳情况下，指数计数的累积
样板
结构计数
：std:：conditional:：type
{};
//从与Idx匹配的Idx的第一个值中获取值
样板
结构优先：std:：整型常量
{};
样板
结构优先
：std:：conditional:：type
{};
//返回匹配Idx的Idx中的所有值是否为tgt
样板
struct AllMatchTarget:std:：true\u类型
{};
样板
结构AllMatchTarget
：std:：conditional:：type
{};
/*根据计数、索引和值生成维度*/
样板
结构GenDims；
样板
结构GenDims{
使用类型=R；
};
样板
结构GenDims
{
静态constexpr auto value=First:：value；
静态断言（AllMatchTarget:：value，
“索引与匹配维度不对应”）；
使用type=typename<
指数,指数,，
联盟、价值观，
typename std:：conditional:：type>：：type；
};
/*把它们放在一起*/
样板
结构收缩型；
样板
结构收缩类型{
静态断言（sizeof…（索引）=sizeof…（值），
“索引数量和维度不匹配”）；
使用计数=计数；
使用type=typename GenDims:：type；
};
静态断言（std:：is_same:：value，“”）；
静态断言（std:：is_same:：value，“”）；
静态断言（std:：is_same:：value，“”）；
静态断言（std:：is_same:：value，“”）；
//未注释时的错误
/*静态断言（std:：is_same这是一个混乱，但我认为它做了您希望它做的事情。几乎可以肯定可以对此进行许多简化，但这是我第一次通过测试。请注意，这并没有实现收缩，只是确定了应该是什么类型。如果这不是您需要的，我在adv中道歉恩斯
#include <type_traits>

template <std::size_t...>
struct Indices {};

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

// Count number of 'i' in 'rest...', base case
template <std::size_t i, std::size_t... rest>
struct Count : std::integral_constant<std::size_t, 0>
{};

// Count number of 'i' in 'rest...', inductive case
template <std::size_t i, std::size_t j, std::size_t... rest>
struct Count<i, j, rest...> :
    std::integral_constant<std::size_t,
                           Count<i, rest...>::value + ((i == j) ? 1 : 0)>
{};

// Is 'i' contained in 'rest...'?
template <std::size_t i, std::size_t... rest>
struct Contains :
    std::integral_constant<bool, (Count<i, rest...>::value > 0)>
{};


// Accumulation of counts of indices in all, base case
template <typename All, typename Remainder,
          typename AccIdx, typename AccCount>
struct Counts {
    using indices = AccIdx;
    using counts = AccCount;
};

// Accumulation of counts of indices in all, inductive case
template <std::size_t... all, std::size_t i, std::size_t... rest,
          std::size_t... indices, std::size_t... counts>
struct Counts<Indices<all...>, Indices<i, rest...>,
              Indices<indices...>, Indices<counts...>>
    : std::conditional<Contains<i, indices...>::value,
                       Counts<Indices<all...>, Indices<rest...>,
                              Indices<indices...>,
                              Indices<counts...>>,
                       Counts<Indices<all...>, Indices<rest...>,
                              Indices<indices..., i>,
                              Indices<counts...,
                                      Count<i, all...>::value>>>::type
{};

// Get value in From that matched the first value of Idx that matched idx
template <std::size_t idx, typename Idx, typename From>
struct First : std::integral_constant<std::size_t, 0>
{};
template <std::size_t i, std::size_t j, std::size_t k,
          std::size_t... indices, std::size_t... values>
struct First<i, Indices<j, indices...>, Indices<k, values...>>
    : std::conditional<i == j,
                       std::integral_constant<std::size_t, k>,
                       First<i, Indices<indices...>,
                             Indices<values...>>>::type
{};

// Return whether all values in From that match Idx being idx are tgt
template <std::size_t idx, std::size_t tgt, typename Idx, typename From>
struct AllMatchTarget : std::true_type
{};
template <std::size_t idx, std::size_t tgt,
          std::size_t i, std::size_t j,
          std::size_t... indices, std::size_t... values>
struct AllMatchTarget<idx, tgt,
                      Indices<i, indices...>, Indices<j, values...>>
    : std::conditional<i == idx && j != tgt, std::false_type,
                       AllMatchTarget<idx, tgt, Indices<indices...>,
                                      Indices<values...>>>::type
{};

/* Generate the dimensions, given the counts, indices, and values */
template <typename Counts, typename Indices,
          typename AllIndices, typename Values, typename Accum>
struct GenDims;

template <typename A, typename V, typename R>
struct GenDims<Indices<>, Indices<>, A, V, R> {
    using type = R;
};
template <typename T, std::size_t i, std::size_t c,
          std::size_t... counts, std::size_t... indices,
          std::size_t... dims, typename AllIndices, typename Values>
struct GenDims<Indices<c, counts...>, Indices<i, indices...>,
               AllIndices, Values, Array<T, dims...>>
{
    static constexpr auto value = First<i, AllIndices, Values>::value;
    static_assert(AllMatchTarget<i, value, AllIndices, Values>::value,
                  "Index doesn't correspond to matching dimensions");
    using type = typename GenDims<
        Indices<counts...>, Indices<indices...>,
        AllIndices, Values,
        typename std::conditional<c == 1,
                                  Array<T, dims..., value>,
                                  Array<T, dims...>>::type>::type;
};

/* Put it all together */
template <typename I, typename A>
struct ContractionType;

template <typename T, std::size_t... indices, std::size_t... values>
struct ContractionType<Indices<indices...>, Array<T, values...>> {
    static_assert(sizeof...(indices) == sizeof...(values),
                   "Number of indices and dimensions do not match");
    using counts = Counts<Indices<indices...>,
                          Indices<indices...>,
                          Indices<>, Indices<>>;
    using type = typename GenDims<typename counts::counts,
                                  typename counts::indices,
                                  Indices<indices...>, Indices<values...>,
                                  Array<T>>::type;
};

static_assert(std::is_same<typename
              ContractionType<Indices<0, 0>, Array<double, 3, 3>>::type,
              Array<double>>::value, "");
static_assert(std::is_same<typename
              ContractionType<Indices<0, 1>, Array<double, 3, 3>>::type,
              Array<double, 3, 3>>::value, "");
static_assert(std::is_same<typename
              ContractionType<Indices<0, 1, 0>, Array<double, 3, 4, 3>>::type,
              Array<double, 4>>::value, "");
static_assert(std::is_same<typename
              ContractionType<Indices<0, 1, 0, 7, 7, 2>,
              Array<double, 3, 4, 3, 5, 5, 6>>::type,
              Array<double, 4, 6>>::value, "");

// Errors appropriately when uncommented
/* static_assert(std::is_same<typename */
/*               ContractionType<Indices<10,10, 2, 3>, */
/*               Array<double, 5,6,4,4>>::type, */
/*               Array<double>::value, ""); */

#包括
样板
结构索引{}；
样板
结构数组{}；
//在“rest…”中计算“i”的数目，基本情况
样板
结构计数：标准：：整型常量
{};
//计数“rest…”中的“i”个数，归纳情况
样板
结构计数：
积分常数
{};
//“我”是否包含在“休息…”中？
样板
结构包含：
标准：积分（常数0）>
{};
//所有基本情况下的指数计数累积
样板
结构计数{
使用指数=AccIdx；
使用计数=AccCount；
};
//在所有归纳情况下，指数计数的累积
样板
结构计数
：std:：conditional:：type
{};
//从与Idx匹配的Idx的第一个值中获取值
样板
结构优先：std:：整型常量
{};
T
auto arr = contraction(Indices<0,0>, Array<double,3,3>) 
// arr is Array<double> as both indices contract 0==0

auto arr = contraction(Indices<0,1>, Array<double,3,3>) 
// arr is Array<double,3,3> as no contraction happens here, 0!=1

auto arr = contraction(Indices<0,1,0>, Array<double,3,4,3>) 
// arr is Array<double,4> as 1st and 3rd indices contract 0==0  

auto arr = contraction(Indices<0,1,0,7,7,2>, Array<double,3,4,3,5,5,6>) 
// arr is Array<double,4,6> as (1st and 3rd, 0==0) and (4th and 5th, 7==7) indices contract

auto arr = contraction(Indices<10,10,2,3>, Array<double,5,6,4,4>
// should not compile as contraction between 1st and 2nd arguments 
// requested but dimensions don't match 5!=6

// The parameters of Indices really do not matter as long as 
// we can identify contractions. They are typically expressed as enums, I,J,K...

#include <type_traits>

template <std::size_t...>
struct Indices {};

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

// Count number of 'i' in 'rest...', base case
template <std::size_t i, std::size_t... rest>
struct Count : std::integral_constant<std::size_t, 0>
{};

// Count number of 'i' in 'rest...', inductive case
template <std::size_t i, std::size_t j, std::size_t... rest>
struct Count<i, j, rest...> :
    std::integral_constant<std::size_t,
                           Count<i, rest...>::value + ((i == j) ? 1 : 0)>
{};

// Is 'i' contained in 'rest...'?
template <std::size_t i, std::size_t... rest>
struct Contains :
    std::integral_constant<bool, (Count<i, rest...>::value > 0)>
{};


// Accumulation of counts of indices in all, base case
template <typename All, typename Remainder,
          typename AccIdx, typename AccCount>
struct Counts {
    using indices = AccIdx;
    using counts = AccCount;
};

// Accumulation of counts of indices in all, inductive case
template <std::size_t... all, std::size_t i, std::size_t... rest,
          std::size_t... indices, std::size_t... counts>
struct Counts<Indices<all...>, Indices<i, rest...>,
              Indices<indices...>, Indices<counts...>>
    : std::conditional<Contains<i, indices...>::value,
                       Counts<Indices<all...>, Indices<rest...>,
                              Indices<indices...>,
                              Indices<counts...>>,
                       Counts<Indices<all...>, Indices<rest...>,
                              Indices<indices..., i>,
                              Indices<counts...,
                                      Count<i, all...>::value>>>::type
{};

// Get value in From that matched the first value of Idx that matched idx
template <std::size_t idx, typename Idx, typename From>
struct First : std::integral_constant<std::size_t, 0>
{};
template <std::size_t i, std::size_t j, std::size_t k,
          std::size_t... indices, std::size_t... values>
struct First<i, Indices<j, indices...>, Indices<k, values...>>
    : std::conditional<i == j,
                       std::integral_constant<std::size_t, k>,
                       First<i, Indices<indices...>,
                             Indices<values...>>>::type
{};

// Return whether all values in From that match Idx being idx are tgt
template <std::size_t idx, std::size_t tgt, typename Idx, typename From>
struct AllMatchTarget : std::true_type
{};
template <std::size_t idx, std::size_t tgt,
          std::size_t i, std::size_t j,
          std::size_t... indices, std::size_t... values>
struct AllMatchTarget<idx, tgt,
                      Indices<i, indices...>, Indices<j, values...>>
    : std::conditional<i == idx && j != tgt, std::false_type,
                       AllMatchTarget<idx, tgt, Indices<indices...>,
                                      Indices<values...>>>::type
{};

/* Generate the dimensions, given the counts, indices, and values */
template <typename Counts, typename Indices,
          typename AllIndices, typename Values, typename Accum>
struct GenDims;

template <typename A, typename V, typename R>
struct GenDims<Indices<>, Indices<>, A, V, R> {
    using type = R;
};
template <typename T, std::size_t i, std::size_t c,
          std::size_t... counts, std::size_t... indices,
          std::size_t... dims, typename AllIndices, typename Values>
struct GenDims<Indices<c, counts...>, Indices<i, indices...>,
               AllIndices, Values, Array<T, dims...>>
{
    static constexpr auto value = First<i, AllIndices, Values>::value;
    static_assert(AllMatchTarget<i, value, AllIndices, Values>::value,
                  "Index doesn't correspond to matching dimensions");
    using type = typename GenDims<
        Indices<counts...>, Indices<indices...>,
        AllIndices, Values,
        typename std::conditional<c == 1,
                                  Array<T, dims..., value>,
                                  Array<T, dims...>>::type>::type;
};

/* Put it all together */
template <typename I, typename A>
struct ContractionType;

template <typename T, std::size_t... indices, std::size_t... values>
struct ContractionType<Indices<indices...>, Array<T, values...>> {
    static_assert(sizeof...(indices) == sizeof...(values),
                   "Number of indices and dimensions do not match");
    using counts = Counts<Indices<indices...>,
                          Indices<indices...>,
                          Indices<>, Indices<>>;
    using type = typename GenDims<typename counts::counts,
                                  typename counts::indices,
                                  Indices<indices...>, Indices<values...>,
                                  Array<T>>::type;
};

static_assert(std::is_same<typename
              ContractionType<Indices<0, 0>, Array<double, 3, 3>>::type,
              Array<double>>::value, "");
static_assert(std::is_same<typename
              ContractionType<Indices<0, 1>, Array<double, 3, 3>>::type,
              Array<double, 3, 3>>::value, "");
static_assert(std::is_same<typename
              ContractionType<Indices<0, 1, 0>, Array<double, 3, 4, 3>>::type,
              Array<double, 4>>::value, "");
static_assert(std::is_same<typename
              ContractionType<Indices<0, 1, 0, 7, 7, 2>,
              Array<double, 3, 4, 3, 5, 5, 6>>::type,
              Array<double, 4, 6>>::value, "");

// Errors appropriately when uncommented
/* static_assert(std::is_same<typename */
/*               ContractionType<Indices<10,10, 2, 3>, */
/*               Array<double, 5,6,4,4>>::type, */
/*               Array<double>::value, ""); */

// is ind[i] unique in ind?
template<size_t N>
constexpr bool is_uniq(const int (&ind)[N], size_t i, size_t cur = 0){
    return cur == N ? true : 
           (cur == i || ind[cur] != ind[i]) ? is_uniq(ind, i, cur + 1) : false;
}

// For every i where ind[i] == index, is dim[i] == dimension?
template<size_t N>
constexpr bool check_all_eq(int index, int dimension,
                            const int (&ind)[N], const int (&dim)[N], size_t cur = 0) {
    return cur == N ? true :
           (ind[cur] != index || dim[cur] == dimension) ? 
                check_all_eq(index, dimension, ind, dim, cur + 1) : false;
}

// if position i should be contracted away, return -1, otherwise return dim[i].
// triggers a compile-time error when used in a constant expression on mismatch.
template<size_t N>
constexpr int calc(size_t i, const int (&ind)[N], const int (&dim)[N]){
    return is_uniq(ind, i) ? dim[i] :
           check_all_eq(ind[i], dim[i], ind, dim) ? -1 : throw "dimension mismatch";
}

template<class Ind, class... Inds>
struct concat { using type = Ind; };
template<int... I1, int... I2, class... Inds>
struct concat<Indices<I1...>, Indices<I2...>, Inds...>
    :  concat<Indices<I1..., I2...>, Inds...> {};

// filter out all instances of I from Is...,
// return the rest as an Indices    
template<int I, int... Is>
struct filter
    :  concat<typename std::conditional<Is == I, Indices<>, Indices<Is>>::type...> {};

template<class Ind, class Arr, class Seq>
struct contraction_impl;

template<class T, int... Ind, int... Dim, size_t... Seq>
struct contraction_impl<Indices<Ind...>, Array<T, Dim...>, std::index_sequence<Seq...>>{
    static constexpr int ind[] = { Ind... };
    static constexpr int dim[] = { Dim... };
    static constexpr int result[] = {calc(Seq, ind, dim)...};

    template<int... Dims>
    static auto unpack_helper(Indices<Dims...>) -> Array<T, Dims...>;

    using type = decltype(unpack_helper(typename filter<-1,  result[Seq]...>::type{}));
};


template<class T, int ... Dims, int ... Idx, 
typename std::enable_if<sizeof...(Dims)==sizeof...(Idx),bool>::type=0>
typename contraction_impl<Indices<Idx...>, Array<T,Dims...>, 
                          std::make_index_sequence<sizeof...(Dims)>>::type
contraction(const Indices<Idx...> &idx, const Array<T,Dims...> &a);