eigen/Eigen/src/Core/util/MoreMeta.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_MOREMETA_H
#define EIGEN_MOREMETA_H

// IWYU pragma: private
#include "../InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

template <typename... tt>
struct type_list {
  constexpr static int count = sizeof...(tt);
};

template <typename t, typename... tt>
struct type_list<t, tt...> {
  constexpr static int count = sizeof...(tt) + 1;
  typedef t first_type;
};

template <typename T, T... nn>
struct numeric_list {
  constexpr static std::size_t count = sizeof...(nn);
};

template <typename T, T n, T... nn>
struct numeric_list<T, n, nn...> {
  static constexpr std::size_t count = sizeof...(nn) + 1;
  static constexpr T first_value = n;
};

// Ddoxygen doesn't like the recursive definition of gen_numeric_list.
#ifndef EIGEN_PARSED_BY_DOXYGEN
/* numeric list constructors
 *
 * equivalencies:
 *     constructor                                              result
 *     typename gen_numeric_list<int, 5>::type                  numeric_list<int, 0,1,2,3,4>
 *     typename gen_numeric_list_reversed<int, 5>::type         numeric_list<int, 4,3,2,1,0>
 *     typename gen_numeric_list_swapped_pair<int, 5,1,2>::type numeric_list<int, 0,2,1,3,4>
 *     typename gen_numeric_list_repeated<int, 0, 5>::type      numeric_list<int, 0,0,0,0,0>
 */

template <typename T, std::size_t n, T start = 0, T... ii>
struct gen_numeric_list : gen_numeric_list<T, n - 1, start, start + n - 1, ii...> {};

template <typename T, T start, T... ii>
struct gen_numeric_list<T, 0, start, ii...> {
  typedef numeric_list<T, ii...> type;
};

template <typename T, std::size_t n, T start = 0, T... ii>
struct gen_numeric_list_reversed : gen_numeric_list_reversed<T, n - 1, start, ii..., start + n - 1> {};
template <typename T, T start, T... ii>
struct gen_numeric_list_reversed<T, 0, start, ii...> {
  typedef numeric_list<T, ii...> type;
};

template <typename T, std::size_t n, T a, T b, T start = 0, T... ii>
struct gen_numeric_list_swapped_pair
    : gen_numeric_list_swapped_pair<T, n - 1, a, b, start,
                                    (start + n - 1) == a ? b : ((start + n - 1) == b ? a : (start + n - 1)), ii...> {};
template <typename T, T a, T b, T start, T... ii>
struct gen_numeric_list_swapped_pair<T, 0, a, b, start, ii...> {
  typedef numeric_list<T, ii...> type;
};

template <typename T, std::size_t n, T V, T... nn>
struct gen_numeric_list_repeated : gen_numeric_list_repeated<T, n - 1, V, V, nn...> {};
template <typename T, T V, T... nn>
struct gen_numeric_list_repeated<T, 0, V, nn...> {
  typedef numeric_list<T, nn...> type;
};
#else
template <typename T, std::size_t n, T start = 0, T... ii>
struct gen_numeric_list;
#endif  // not EIGEN_PARSED_BY_DOXYGEN

/* list manipulation: concatenate */

template <class a, class b>
struct concat;

template <typename... as, typename... bs>
struct concat<type_list<as...>, type_list<bs...>> {
  typedef type_list<as..., bs...> type;
};
template <typename T, T... as, T... bs>
struct concat<numeric_list<T, as...>, numeric_list<T, bs...>> {
  typedef numeric_list<T, as..., bs...> type;
};

template <typename... p>
struct mconcat;
template <typename a>
struct mconcat<a> {
  typedef a type;
};
template <typename a, typename b>
struct mconcat<a, b> : concat<a, b> {};
template <typename a, typename b, typename... cs>
struct mconcat<a, b, cs...> : concat<a, typename mconcat<b, cs...>::type> {};

/* list manipulation: extract slices */

template <int n, typename x>
struct take;

template <int n, typename a, typename... as>
struct take<n, type_list<a, as...>> : concat<type_list<a>, typename take<n - 1, type_list<as...>>::type> {};

template <int n>
struct take<n, type_list<>> {
  typedef type_list<> type;
};

template <typename a, typename... as>
struct take<0, type_list<a, as...>> {
  typedef type_list<> type;
};

template <>
struct take<0, type_list<>> {
  typedef type_list<> type;
};

template <typename T, int n, T a, T... as>
struct take<n, numeric_list<T, a, as...>>
    : concat<numeric_list<T, a>, typename take<n - 1, numeric_list<T, as...>>::type> {};

template <typename T, T a, T... as>
struct take<0, numeric_list<T, a, as...>> {
  typedef numeric_list<T> type;
};

template <typename T>
struct take<0, numeric_list<T>> {
  typedef numeric_list<T> type;
};

template <typename T, int n, T... ii>
struct h_skip_helper_numeric;
template <typename T, int n, T i, T... ii>
struct h_skip_helper_numeric<T, n, i, ii...> : h_skip_helper_numeric<T, n - 1, ii...> {};
template <typename T, T i, T... ii>
struct h_skip_helper_numeric<T, 0, i, ii...> {
  typedef numeric_list<T, i, ii...> type;
};
template <typename T, int n>
struct h_skip_helper_numeric<T, n> {
  typedef numeric_list<T> type;
};
template <typename T>
struct h_skip_helper_numeric<T, 0> {
  typedef numeric_list<T> type;
};

template <int n, typename... tt>
struct h_skip_helper_type;
template <int n, typename t, typename... tt>
struct h_skip_helper_type<n, t, tt...> : h_skip_helper_type<n - 1, tt...> {};
template <typename t, typename... tt>
struct h_skip_helper_type<0, t, tt...> {
  typedef type_list<t, tt...> type;
};
template <int n>
struct h_skip_helper_type<n> {
  typedef type_list<> type;
};
template <>
struct h_skip_helper_type<0> {
  typedef type_list<> type;
};

template <int n>
struct h_skip {
  template <typename T, T... ii>
  constexpr static typename h_skip_helper_numeric<T, n, ii...>::type helper(numeric_list<T, ii...>) {
    return typename h_skip_helper_numeric<T, n, ii...>::type();
  }
  template <typename... tt>
  constexpr static typename h_skip_helper_type<n, tt...>::type helper(type_list<tt...>) {
    return typename h_skip_helper_type<n, tt...>::type();
  }
};

template <int n, typename a>
struct skip {
  typedef decltype(h_skip<n>::helper(a())) type;
};

template <int start, int count, typename a>
struct slice : take<count, typename skip<start, a>::type> {};

/* list manipulation: retrieve single element from list */

template <int n, typename x>
struct get;

template <int n, typename a, typename... as>
struct get<n, type_list<a, as...>> : get<n - 1, type_list<as...>> {};
template <typename a, typename... as>
struct get<0, type_list<a, as...>> {
  typedef a type;
};

template <typename T, int n, T a, T... as>
struct get<n, numeric_list<T, a, as...>> : get<n - 1, numeric_list<T, as...>> {};
template <typename T, T a, T... as>
struct get<0, numeric_list<T, a, as...>> {
  constexpr static T value = a;
};

template <std::size_t n, typename T, T a, T... as>
constexpr T array_get(const numeric_list<T, a, as...>&) {
  return get<(int)n, numeric_list<T, a, as...>>::value;
}

/* always get type, regardless of dummy; good for parameter pack expansion */

template <typename T, T dummy, typename t>
struct id_numeric {
  typedef t type;
};
template <typename dummy, typename t>
struct id_type {
  typedef t type;
};

/* equality checking, flagged version */

template <typename a, typename b>
struct is_same_gf : is_same<a, b> {
  constexpr static int global_flags = 0;
};

/* apply_op to list */

template <bool from_left,  // false
          template <typename, typename> class op, typename additional_param, typename... values>
struct h_apply_op_helper {
  typedef type_list<typename op<values, additional_param>::type...> type;
};
template <template <typename, typename> class op, typename additional_param, typename... values>
struct h_apply_op_helper<true, op, additional_param, values...> {
  typedef type_list<typename op<additional_param, values>::type...> type;
};

template <bool from_left, template <typename, typename> class op, typename additional_param>
struct h_apply_op {
  template <typename... values>
  constexpr static typename h_apply_op_helper<from_left, op, additional_param, values...>::type helper(
      type_list<values...>) {
    return typename h_apply_op_helper<from_left, op, additional_param, values...>::type();
  }
};

template <template <typename, typename> class op, typename additional_param, typename a>
struct apply_op_from_left {
  typedef decltype(h_apply_op<true, op, additional_param>::helper(a())) type;
};

template <template <typename, typename> class op, typename additional_param, typename a>
struct apply_op_from_right {
  typedef decltype(h_apply_op<false, op, additional_param>::helper(a())) type;
};

/* see if an element is in a list */

template <template <typename, typename> class test, typename check_against, typename h_list,
          bool last_check_positive = false>
struct contained_in_list;

template <template <typename, typename> class test, typename check_against, typename h_list>
struct contained_in_list<test, check_against, h_list, true> {
  constexpr static bool value = true;
};

template <template <typename, typename> class test, typename check_against, typename a, typename... as>
struct contained_in_list<test, check_against, type_list<a, as...>, false>
    : contained_in_list<test, check_against, type_list<as...>, test<check_against, a>::value> {};

template <template <typename, typename> class test, typename check_against, typename... empty>
struct contained_in_list<test, check_against, type_list<empty...>, false> {
  constexpr static bool value = false;
};

/* see if an element is in a list and check for global flags */

template <template <typename, typename> class test, typename check_against, typename h_list, int default_flags = 0,
          bool last_check_positive = false, int last_check_flags = default_flags>
struct contained_in_list_gf;

template <template <typename, typename> class test, typename check_against, typename h_list, int default_flags,
          int last_check_flags>
struct contained_in_list_gf<test, check_against, h_list, default_flags, true, last_check_flags> {
  constexpr static bool value = true;
  constexpr static int global_flags = last_check_flags;
};

template <template <typename, typename> class test, typename check_against, typename a, typename... as,
          int default_flags, int last_check_flags>
struct contained_in_list_gf<test, check_against, type_list<a, as...>, default_flags, false, last_check_flags>
    : contained_in_list_gf<test, check_against, type_list<as...>, default_flags, test<check_against, a>::value,
                           test<check_against, a>::global_flags> {};

template <template <typename, typename> class test, typename check_against, typename... empty, int default_flags,
          int last_check_flags>
struct contained_in_list_gf<test, check_against, type_list<empty...>, default_flags, false, last_check_flags> {
  constexpr static bool value = false;
  constexpr static int global_flags = default_flags;
};

/* generic reductions */

template <typename Reducer, typename... Ts>
struct reduce;

template <typename Reducer>
struct reduce<Reducer> {
  EIGEN_DEVICE_FUNC constexpr static int run() { return Reducer::Identity; }
};

template <typename Reducer, typename A>
struct reduce<Reducer, A> {
  EIGEN_DEVICE_FUNC constexpr static A run(A a) { return a; }
};

template <typename Reducer, typename A, typename... Ts>
struct reduce<Reducer, A, Ts...> {
  EIGEN_DEVICE_FUNC constexpr static auto run(A a, Ts... ts)
      -> decltype(Reducer::run(a, reduce<Reducer, Ts...>::run(ts...))) {
    return Reducer::run(a, reduce<Reducer, Ts...>::run(ts...));
  }
};

/* generic binary operations */

struct sum_op {
  template <typename A, typename B>
  EIGEN_DEVICE_FUNC constexpr static auto run(A a, B b) -> decltype(a + b) {
    return a + b;
  }
  static constexpr int Identity = 0;
};
struct product_op {
  template <typename A, typename B>
  EIGEN_DEVICE_FUNC constexpr static auto run(A a, B b) -> decltype(a * b) {
    return a * b;
  }
  static constexpr int Identity = 1;
};

struct logical_and_op {
  template <typename A, typename B>
  constexpr static auto run(A a, B b) -> decltype(a && b) {
    return a && b;
  }
};
struct logical_or_op {
  template <typename A, typename B>
  constexpr static auto run(A a, B b) -> decltype(a || b) {
    return a || b;
  }
};

struct equal_op {
  template <typename A, typename B>
  constexpr static auto run(A a, B b) -> decltype(a == b) {
    return a == b;
  }
};
struct not_equal_op {
  template <typename A, typename B>
  constexpr static auto run(A a, B b) -> decltype(a != b) {
    return a != b;
  }
};
struct lesser_op {
  template <typename A, typename B>
  constexpr static auto run(A a, B b) -> decltype(a < b) {
    return a < b;
  }
};
struct lesser_equal_op {
  template <typename A, typename B>
  constexpr static auto run(A a, B b) -> decltype(a <= b) {
    return a <= b;
  }
};
struct greater_op {
  template <typename A, typename B>
  constexpr static auto run(A a, B b) -> decltype(a > b) {
    return a > b;
  }
};
struct greater_equal_op {
  template <typename A, typename B>
  constexpr static auto run(A a, B b) -> decltype(a >= b) {
    return a >= b;
  }
};

/* generic unary operations */

struct not_op {
  template <typename A>
  constexpr static auto run(A a) -> decltype(!a) {
    return !a;
  }
};
struct negation_op {
  template <typename A>
  constexpr static auto run(A a) -> decltype(-a) {
    return -a;
  }
};
struct greater_equal_zero_op {
  template <typename A>
  constexpr static auto run(A a) -> decltype(a >= 0) {
    return a >= 0;
  }
};

/* reductions for lists */

// using auto -> return value spec makes ICC 13.0 and 13.1 crash here, so we have to hack it
// together in front... (13.0 doesn't work with array_prod/array_reduce/... anyway, but 13.1
// does...
template <typename... Ts>
EIGEN_DEVICE_FUNC constexpr decltype(reduce<product_op, Ts...>::run((*((Ts*)0))...)) arg_prod(Ts... ts) {
  return reduce<product_op, Ts...>::run(ts...);
}

template <typename... Ts>
constexpr decltype(reduce<sum_op, Ts...>::run((*((Ts*)0))...)) arg_sum(Ts... ts) {
  return reduce<sum_op, Ts...>::run(ts...);
}

/* reverse arrays */

template <typename Array, int... n>
constexpr Array h_array_reverse(Array arr, numeric_list<int, n...>) {
  return {{array_get<sizeof...(n) - n - 1>(arr)...}};
}

template <typename T, std::size_t N>
constexpr array<T, N> array_reverse(array<T, N> arr) {
  return h_array_reverse(arr, typename gen_numeric_list<int, N>::type());
}

/* generic array reductions */

// can't reuse standard reduce() interface above because Intel's Compiler
// *really* doesn't like it, so we just reimplement the stuff
// (start from N - 1 and work down to 0 because specialization for
// n == N - 1 also doesn't work in Intel's compiler, so it goes into
// an infinite loop)
template <typename Reducer, typename T, std::size_t N, std::size_t n = N - 1>
struct h_array_reduce {
  EIGEN_DEVICE_FUNC constexpr static auto run(array<T, N> arr, T identity)
      -> decltype(Reducer::run(h_array_reduce<Reducer, T, N, n - 1>::run(arr, identity), array_get<n>(arr))) {
    return Reducer::run(h_array_reduce<Reducer, T, N, n - 1>::run(arr, identity), array_get<n>(arr));
  }
};

template <typename Reducer, typename T, std::size_t N>
struct h_array_reduce<Reducer, T, N, 0> {
  EIGEN_DEVICE_FUNC constexpr static T run(const array<T, N>& arr, T) { return array_get<0>(arr); }
};

template <typename Reducer, typename T>
struct h_array_reduce<Reducer, T, 0> {
  EIGEN_DEVICE_FUNC constexpr static T run(const array<T, 0>&, T identity) { return identity; }
};

template <typename Reducer, typename T, std::size_t N>
EIGEN_DEVICE_FUNC constexpr auto array_reduce(const array<T, N>& arr, T identity)
    -> decltype(h_array_reduce<Reducer, T, N>::run(arr, identity)) {
  return h_array_reduce<Reducer, T, N>::run(arr, identity);
}

/* standard array reductions */

template <typename T, std::size_t N>
EIGEN_DEVICE_FUNC constexpr auto array_sum(const array<T, N>& arr)
    -> decltype(array_reduce<sum_op, T, N>(arr, static_cast<T>(0))) {
  return array_reduce<sum_op, T, N>(arr, static_cast<T>(0));
}

template <typename T, std::size_t N>
EIGEN_DEVICE_FUNC constexpr auto array_prod(const array<T, N>& arr)
    -> decltype(array_reduce<product_op, T, N>(arr, static_cast<T>(1))) {
  return array_reduce<product_op, T, N>(arr, static_cast<T>(1));
}

template <typename t>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE t array_prod(const std::vector<t>& a) {
  eigen_assert(a.size() > 0);
  t prod = 1;
  for (size_t i = 0; i < a.size(); ++i) {
    prod *= a[i];
  }
  return prod;
}

/* zip an array */

template <typename Op, typename A, typename B, std::size_t N, int... n>
constexpr array<decltype(Op::run(A(), B())), N> h_array_zip(array<A, N> a, array<B, N> b, numeric_list<int, n...>) {
  return array<decltype(Op::run(A(), B())), N>{{Op::run(array_get<n>(a), array_get<n>(b))...}};
}

template <typename Op, typename A, typename B, std::size_t N>
constexpr array<decltype(Op::run(A(), B())), N> array_zip(array<A, N> a, array<B, N> b) {
  return h_array_zip<Op>(a, b, typename gen_numeric_list<int, N>::type());
}

/* zip an array and reduce the result */

template <typename Reducer, typename Op, typename A, typename B, std::size_t N, int... n>
constexpr auto h_array_zip_and_reduce(array<A, N> a, array<B, N> b, numeric_list<int, n...>)
    -> decltype(reduce<Reducer, typename id_numeric<int, n, decltype(Op::run(A(), B()))>::type...>::run(
        Op::run(array_get<n>(a), array_get<n>(b))...)) {
  return reduce<Reducer, typename id_numeric<int, n, decltype(Op::run(A(), B()))>::type...>::run(
      Op::run(array_get<n>(a), array_get<n>(b))...);
}

template <typename Reducer, typename Op, typename A, typename B, std::size_t N>
constexpr auto array_zip_and_reduce(array<A, N> a, array<B, N> b)
    -> decltype(h_array_zip_and_reduce<Reducer, Op, A, B, N>(a, b, typename gen_numeric_list<int, N>::type())) {
  return h_array_zip_and_reduce<Reducer, Op, A, B, N>(a, b, typename gen_numeric_list<int, N>::type());
}

/* apply stuff to an array */

template <typename Op, typename A, std::size_t N, int... n>
constexpr array<decltype(Op::run(A())), N> h_array_apply(array<A, N> a, numeric_list<int, n...>) {
  return array<decltype(Op::run(A())), N>{{Op::run(array_get<n>(a))...}};
}

template <typename Op, typename A, std::size_t N>
constexpr array<decltype(Op::run(A())), N> array_apply(array<A, N> a) {
  return h_array_apply<Op>(a, typename gen_numeric_list<int, N>::type());
}

/* apply stuff to an array and reduce */

template <typename Reducer, typename Op, typename A, std::size_t N, int... n>
constexpr auto h_array_apply_and_reduce(array<A, N> arr, numeric_list<int, n...>)
    -> decltype(reduce<Reducer, typename id_numeric<int, n, decltype(Op::run(A()))>::type...>::run(
        Op::run(array_get<n>(arr))...)) {
  return reduce<Reducer, typename id_numeric<int, n, decltype(Op::run(A()))>::type...>::run(
      Op::run(array_get<n>(arr))...);
}

template <typename Reducer, typename Op, typename A, std::size_t N>
constexpr auto array_apply_and_reduce(array<A, N> a)
    -> decltype(h_array_apply_and_reduce<Reducer, Op, A, N>(a, typename gen_numeric_list<int, N>::type())) {
  return h_array_apply_and_reduce<Reducer, Op, A, N>(a, typename gen_numeric_list<int, N>::type());
}

/* repeat a value n times (and make an array out of it
 * usage:
 *   array<int, 16> = repeat<16>(42);
 */

template <int n>
struct h_repeat {
  template <typename t, int... ii>
  constexpr static array<t, n> run(t v, numeric_list<int, ii...>) {
    return {{typename id_numeric<int, ii, t>::type(v)...}};
  }
};

template <int n, typename t>
constexpr array<t, n> repeat(t v) {
  return h_repeat<n>::run(v, typename gen_numeric_list<int, n>::type());
}

/* instantiate a class by a C-style array */
template <class InstType, typename ArrType, std::size_t N, bool Reverse, typename... Ps>
struct h_instantiate_by_c_array;

template <class InstType, typename ArrType, std::size_t N, typename... Ps>
struct h_instantiate_by_c_array<InstType, ArrType, N, false, Ps...> {
  static InstType run(ArrType* arr, Ps... args) {
    return h_instantiate_by_c_array<InstType, ArrType, N - 1, false, Ps..., ArrType>::run(arr + 1, args..., arr[0]);
  }
};

template <class InstType, typename ArrType, std::size_t N, typename... Ps>
struct h_instantiate_by_c_array<InstType, ArrType, N, true, Ps...> {
  static InstType run(ArrType* arr, Ps... args) {
    return h_instantiate_by_c_array<InstType, ArrType, N - 1, false, ArrType, Ps...>::run(arr + 1, arr[0], args...);
  }
};

template <class InstType, typename ArrType, typename... Ps>
struct h_instantiate_by_c_array<InstType, ArrType, 0, false, Ps...> {
  static InstType run(ArrType* arr, Ps... args) {
    (void)arr;
    return InstType(args...);
  }
};

template <class InstType, typename ArrType, typename... Ps>
struct h_instantiate_by_c_array<InstType, ArrType, 0, true, Ps...> {
  static InstType run(ArrType* arr, Ps... args) {
    (void)arr;
    return InstType(args...);
  }
};

template <class InstType, typename ArrType, std::size_t N, bool Reverse = false>
InstType instantiate_by_c_array(ArrType* arr) {
  return h_instantiate_by_c_array<InstType, ArrType, N, Reverse>::run(arr);
}

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_MOREMETA_H