tuple.hpp

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// Copyright (c) 2010-2025, Lawrence Livermore National Security, LLC. Produced
// at the Lawrence Livermore National Laboratory. All Rights reserved. See files
// LICENSE and NOTICE for details. LLNL-CODE-806117.
//
// This file is part of the MFEM library. For more information and source code
// availability visit https://mfem.org.
//
// MFEM is free software; you can redistribute it and/or modify it under the
// terms of the BSD-3 license. We welcome feedback and contributions, see file
// CONTRIBUTING.md for details.
#pragma once
 
// This is serac's tuple implementation
 
#include <ostream>
#include "../../config/config.hpp"
#include <utility>
 
// Define a portable unreachable macro
#if defined(__GNUC__) || defined(__clang__)
#if defined(__CUDACC_VER_MAJOR__)
#if __CUDACC_VER_MAJOR__ <= 11 && __CUDACC_VER_MINOR__ < 3
// nvcc didn't add __builtin_unreachable() until cuda 11.3
#define MFEM_UNREACHABLE()
#else
// nvcc >= 11.3
#define MFEM_UNREACHABLE() __builtin_unreachable()
#endif
#else
// host-only version
#define MFEM_UNREACHABLE() __builtin_unreachable()
#endif
#elif defined(_MSC_VER)
#define MFEM_UNREACHABLE() __assume(0)
#endif
 
namespace mfem::future
{
 
/**
 * @tparam T the types stored in the tuple
 * @brief This is a class that mimics most of std::tuple's interface,
 * except that it is usable in CUDA kernels and admits some arithmetic operator overloads.
 *
 * see https://en.cppreference.com/w/cpp/utility/tuple for more information about std::tuple
 */
template <typename... T>
struct tuple
{
};
 
/**
 * @brief Type that mimics std::tuple
 *
 * @tparam T0 The first type stored in the tuple
 */
template <typename T0>
struct tuple<T0>
{
   T0 v0;  ///< The first member of the tuple
};
 
/**
 * @brief Type that mimics std::tuple
 *
 * @tparam T0 The first type stored in the tuple
 * @tparam T1 The second type stored in the tuple
 */
template <typename T0, typename T1>
struct tuple<T0, T1>
{
   T0 v0;  ///< The first member of the tuple
   T1 v1;  ///< The second member of the tuple
};
 
/**
 * @brief Type that mimics std::tuple
 *
 * @tparam T0 The first type stored in the tuple
 * @tparam T1 The second type stored in the tuple
 * @tparam T2 The third type stored in the tuple
 */
template <typename T0, typename T1, typename T2>
struct tuple<T0, T1, T2>
{
   T0 v0;  ///< The first member of the tuple
   T1 v1;  ///< The second member of the tuple
   T2 v2;  ///< The third member of the tuple
};
 
/**
 * @brief Type that mimics std::tuple
 *
 * @tparam T0 The first type stored in the tuple
 * @tparam T1 The second type stored in the tuple
 * @tparam T2 The third type stored in the tuple
 * @tparam T3 The fourth type stored in the tuple
 */
template <typename T0, typename T1, typename T2, typename T3>
struct tuple<T0, T1, T2, T3>
{
   T0 v0;  ///< The first member of the tuple
   T1 v1;  ///< The second member of the tuple
   T2 v2;  ///< The third member of the tuple
   T3 v3;  ///< The fourth member of the tuple
};
 
/**
 * @brief Type that mimics std::tuple
 *
 * @tparam T0 The first type stored in the tuple
 * @tparam T1 The second type stored in the tuple
 * @tparam T2 The third type stored in the tuple
 * @tparam T3 The fourth type stored in the tuple
 * @tparam T4 The fifth type stored in the tuple
 */
template <typename T0, typename T1, typename T2, typename T3, typename T4>
struct tuple<T0, T1, T2, T3, T4>
{
   T0 v0;  ///< The first member of the tuple
   T1 v1;  ///< The second member of the tuple
   T2 v2;  ///< The third member of the tuple
   T3 v3;  ///< The fourth member of the tuple
   T4 v4;  ///< The fifth member of the tuple
};
 
/**
 * @brief Type that mimics std::tuple
 *
 * @tparam T0 The first type stored in the tuple
 * @tparam T1 The second type stored in the tuple
 * @tparam T2 The third type stored in the tuple
 * @tparam T3 The fourth type stored in the tuple
 * @tparam T4 The fifth type stored in the tuple
 * @tparam T5 The sixth type stored in the tuple
 */
template <typename T0, typename T1, typename T2, typename T3, typename T4, typename T5>
struct tuple<T0, T1, T2, T3, T4, T5>
{
   T0 v0;  ///< The first member of the tuple
   T1 v1;  ///< The second member of the tuple
   T2 v2;  ///< The third member of the tuple
   T3 v3;  ///< The fourth member of the tuple
   T4 v4;  ///< The fifth member of the tuple
   T5 v5;  ///< The sixth member of the tuple
};
 
/**
 * @brief Type that mimics std::tuple
 *
 * @tparam T0 The first type stored in the tuple
 * @tparam T1 The second type stored in the tuple
 * @tparam T2 The third type stored in the tuple
 * @tparam T3 The fourth type stored in the tuple
 * @tparam T4 The fifth type stored in the tuple
 * @tparam T5 The sixth type stored in the tuple
 * @tparam T6 The seventh type stored in the tuple
 */
template <typename T0, typename T1, typename T2, typename T3, typename T4, typename T5, typename T6>
struct tuple<T0, T1, T2, T3, T4, T5, T6>
{
   T0 v0;  ///< The first member of the tuple
   T1 v1;  ///< The second member of the tuple
   T2 v2;  ///< The third member of the tuple
   T3 v3;  ///< The fourth member of the tuple
   T4 v4;  ///< The fifth member of the tuple
   T5 v5;  ///< The sixth member of the tuple
   T6 v6;  ///< The seventh member of the tuple
};
 
/**
 * @brief Type that mimics std::tuple
 *
 * @tparam T0 The first type stored in the tuple
 * @tparam T1 The second type stored in the tuple
 * @tparam T2 The third type stored in the tuple
 * @tparam T3 The fourth type stored in the tuple
 * @tparam T4 The fifth type stored in the tuple
 * @tparam T5 The sixth type stored in the tuple
 * @tparam T6 The seventh type stored in the tuple
 * @tparam T7 The eighth type stored in the tuple
 */
template <typename T0, typename T1, typename T2, typename T3, typename T4, typename T5, typename T6, typename T7>
struct tuple<T0, T1, T2, T3, T4, T5, T6, T7>
{
   T0 v0;  ///< The first member of the tuple
   T1 v1;  ///< The second member of the tuple
   T2 v2;  ///< The third member of the tuple
   T3 v3;  ///< The fourth member of the tuple
   T4 v4;  ///< The fifth member of the tuple
   T5 v5;  ///< The sixth member of the tuple
   T6 v6;  ///< The seventh member of the tuple
   T7 v7;  ///< The eighth member of the tuple
};
 
template <typename T0, typename T1, typename T2, typename T3, typename T4, typename T5, typename T6, typename T7, typename T8>
struct tuple<T0, T1, T2, T3, T4, T5, T6, T7, T8>
{
   T0 v0;  ///< The first member of the tuple
   T1 v1;  ///< The second member of the tuple
   T2 v2;  ///< The third member of the tuple
   T3 v3;  ///< The fourth member of the tuple
   T4 v4;  ///< The fifth member of the tuple
   T5 v5;  ///< The sixth member of the tuple
   T6 v6;  ///< The seventh member of the tuple
   T7 v7;  ///< The eighth member of the tuple
   T8 v8;
};
 
/**
 * @brief Class template argument deduction rule for tuples
 * @tparam T The variadic template parameter for tuple types
 */
template <typename... T>
MFEM_HOST_DEVICE
tuple(T...) -> tuple<T...>;
 
/**
 * @brief helper function for combining a list of values into a tuple
 * @tparam T types of the values to be tuple-d
 * @param args the actual values to be put into a tuple
 */
template <typename... T>
MFEM_HOST_DEVICE tuple<T...> make_tuple(const T&... args)
{
   return tuple<T...> {args...};
}
 
template <class... Types>
struct tuple_size
{
};
 
template <class... Types>
struct tuple_size<tuple<Types...>> :
                                std::integral_constant<std::size_t, sizeof...(Types)>
{
};
 
/**
 * @tparam i the tuple index to access
 * @tparam T the types stored in the tuple
 * @brief return a reference to the ith tuple entry
 */
template <int i, typename... T>
MFEM_HOST_DEVICE constexpr auto& get(tuple<T...>& values)
{
   static_assert(i < sizeof...(T));
   if constexpr (i == 0)
   {
      return values.v0;
   }
   if constexpr (i == 1)
   {
      return values.v1;
   }
   if constexpr (i == 2)
   {
      return values.v2;
   }
   if constexpr (i == 3)
   {
      return values.v3;
   }
   if constexpr (i == 4)
   {
      return values.v4;
   }
   if constexpr (i == 5)
   {
      return values.v5;
   }
   if constexpr (i == 6)
   {
      return values.v6;
   }
   if constexpr (i == 7)
   {
      return values.v7;
   }
   if constexpr (i == 8)
   {
      return values.v8;
   }
   MFEM_UNREACHABLE();
}
 
/**
 * @tparam i the tuple index to access
 * @tparam T the types stored in the tuple
 * @brief return a copy of the ith tuple entry
 */
template <int i, typename... T>
MFEM_HOST_DEVICE constexpr const auto& get(const tuple<T...>& values)
{
   static_assert(i < sizeof...(T));
   if constexpr (i == 0)
   {
      return values.v0;
   }
   if constexpr (i == 1)
   {
      return values.v1;
   }
   if constexpr (i == 2)
   {
      return values.v2;
   }
   if constexpr (i == 3)
   {
      return values.v3;
   }
   if constexpr (i == 4)
   {
      return values.v4;
   }
   if constexpr (i == 5)
   {
      return values.v5;
   }
   if constexpr (i == 6)
   {
      return values.v6;
   }
   if constexpr (i == 7)
   {
      return values.v7;
   }
   if constexpr (i == 8)
   {
      return values.v8;
   }
   MFEM_UNREACHABLE();
}
 
/**
 * @brief a function intended to be used for extracting the ith type from a tuple.
 *
 * @note type<i>(my_tuple) returns a value, whereas get<i>(my_tuple) returns a reference
 *
 * @tparam i the index of the tuple to query
 * @tparam T the types stored in the tuple
 * @param values the tuple of values
 * @return a copy of the ith entry of the input
 */
template <int i, typename... T>
MFEM_HOST_DEVICE constexpr auto type(const tuple<T...>& values)
{
   static_assert(i < sizeof...(T));
   if constexpr (i == 0)
   {
      return values.v0;
   }
   if constexpr (i == 1)
   {
      return values.v1;
   }
   if constexpr (i == 2)
   {
      return values.v2;
   }
   if constexpr (i == 3)
   {
      return values.v3;
   }
   if constexpr (i == 4)
   {
      return values.v4;
   }
   if constexpr (i == 5)
   {
      return values.v5;
   }
   if constexpr (i == 6)
   {
      return values.v6;
   }
   if constexpr (i == 7)
   {
      return values.v7;
   }
   if constexpr (i == 8)
   {
      return values.v8;
   }
}
 
/**
 * @brief A helper function for the + operator of tuples
 *
 * @tparam S the types stored in the tuple x
 * @tparam T the types stored in the tuple y
 * @tparam i The integer sequence to i
 * @param x tuple of values
 * @param y tuple of values
 * @return the returned tuple sum
 */
template <typename... S, typename... T, int... i>
MFEM_HOST_DEVICE constexpr auto plus_helper(const tuple<S...>& x,
                                            const tuple<T...>& y,
                                            std::integer_sequence<int, i...>)
{
   return tuple{get<i>(x) + get<i>(y)...};
}
 
/**
 * @tparam S the types stored in the tuple x
 * @tparam T the types stored in the tuple y
 * @param x a tuple of values
 * @param y a tuple of values
 * @brief return a tuple of values defined by elementwise sum of x and y
 */
template <typename... S, typename... T>
MFEM_HOST_DEVICE constexpr auto operator+(const tuple<S...>& x,
                                          const tuple<T...>& y)
{
   static_assert(sizeof...(S) == sizeof...(T));
   return plus_helper(x, y,
                      std::make_integer_sequence<int, static_cast<int>(sizeof...(S))>());
}
 
/**
 * @brief A helper function for the += operator of tuples
 *
 * @tparam T the types stored in the tuples x and y
 * @tparam i integer sequence used to index the tuples
 * @param x tuple of values to be incremented
 * @param y tuple of increment values
 */
template <typename... T, int... i>
MFEM_HOST_DEVICE constexpr void plus_equals_helper(tuple<T...>& x,
                                                   const tuple<T...>& y,
                                                   std::integer_sequence<int, i...>)
{
   ((get<i>(x) += get<i>(y)), ...);
}
 
/**
 * @tparam T the types stored in the tuples x and y
 * @param x a tuple of values
 * @param y a tuple of values
 * @brief add values contained in y, to the tuple x
 */
template <typename... T>
MFEM_HOST_DEVICE constexpr auto operator+=(tuple<T...>& x,
                                           const tuple<T...>& y)
{
   return plus_equals_helper(x, y,
                             std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
}
 
/**
 * @brief A helper function for the -= operator of tuples
 *
 * @tparam T the types stored in the tuples x and y
 * @tparam i integer sequence used to index the tuples
 * @param x tuple of values to be subtracted from
 * @param y tuple of values to subtract from x
 */
template <typename... T, int... i>
MFEM_HOST_DEVICE constexpr void minus_equals_helper(tuple<T...>& x,
                                                    const tuple<T...>& y,
                                                    std::integer_sequence<int, i...>)
{
   ((get<i>(x) -= get<i>(y)), ...);
}
 
/**
 * @tparam T the types stored in the tuples x and y
 * @param x a tuple of values
 * @param y a tuple of values
 * @brief add values contained in y, to the tuple x
 */
template <typename... T>
MFEM_HOST_DEVICE constexpr auto operator-=(tuple<T...>& x,
                                           const tuple<T...>& y)
{
   return minus_equals_helper(x, y,
                              std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
}
 
/**
 * @brief A helper function for the - operator of tuples
 *
 * @tparam S the types stored in the tuple x
 * @tparam T the types stored in the tuple y
 * @tparam i The integer sequence to i
 * @param x tuple of values
 * @param y tuple of values
 * @return the returned tuple difference
 */
template <typename... S, typename... T, int... i>
MFEM_HOST_DEVICE constexpr auto minus_helper(const tuple<S...>& x,
                                             const tuple<T...>& y,
                                             std::integer_sequence<int, i...>)
{
   return tuple{get<i>(x) - get<i>(y)...};
}
 
/**
 * @tparam S the types stored in the tuple x
 * @tparam T the types stored in the tuple y
 * @param x a tuple of values
 * @param y a tuple of values
 * @brief return a tuple of values defined by elementwise difference of x and y
 */
template <typename... S, typename... T>
MFEM_HOST_DEVICE constexpr auto operator-(const tuple<S...>& x,
                                          const tuple<T...>& y)
{
   static_assert(sizeof...(S) == sizeof...(T));
   return minus_helper(x, y,
                       std::make_integer_sequence<int, static_cast<int>(sizeof...(S))>());
}
 
/**
 * @brief A helper function for the - operator of tuples
 *
 * @tparam T the types stored in the tuple y
 * @tparam i The integer sequence to i
 * @param x tuple of values
 * @return the returned tuple difference
 */
template <typename... T, int... i>
MFEM_HOST_DEVICE constexpr auto unary_minus_helper(const tuple<T...>& x,
                                                   std::integer_sequence<int, i...>)
{
   return tuple{-get<i>(x)...};
}
 
/**
 * @tparam T the types stored in the tuple y
 * @param x a tuple of values
 * @brief return a tuple of values defined by applying the unary minus operator to each element of x
 */
template <typename... T>
MFEM_HOST_DEVICE constexpr auto operator-(const tuple<T...>& x)
{
   return unary_minus_helper(x,
                             std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
}
 
/**
 * @brief A helper function for the / operator of tuples
 *
 * @tparam S the types stored in the tuple x
 * @tparam T the types stored in the tuple y
 * @tparam i The integer sequence to i
 * @param x tuple of values
 * @param y tuple of values
 * @return the returned tuple ratio
 */
template <typename... S, typename... T, int... i>
MFEM_HOST_DEVICE constexpr auto div_helper(const tuple<S...>& x,
                                           const tuple<T...>& y,
                                           std::integer_sequence<int, i...>)
{
   return tuple{get<i>(x) / get<i>(y)...};
}
 
/**
 * @tparam S the types stored in the tuple x
 * @tparam T the types stored in the tuple y
 * @param x a tuple of values
 * @param y a tuple of values
 * @brief return a tuple of values defined by elementwise division of x by y
 */
template <typename... S, typename... T>
MFEM_HOST_DEVICE constexpr auto operator/(const tuple<S...>& x,
                                          const tuple<T...>& y)
{
   static_assert(sizeof...(S) == sizeof...(T));
   return div_helper(x, y,
                     std::make_integer_sequence<int, static_cast<int>(sizeof...(S))>());
}
 
/**
 * @brief A helper function for the / operator of tuples
 *
 * @tparam T the types stored in the tuple y
 * @tparam i The integer sequence to i
 * @param x tuple of values
 * @param a the constant numerator
 * @return the returned tuple ratio
 */
template <typename... T, int... i>
MFEM_HOST_DEVICE constexpr auto div_helper(const real_t a,
                                           const tuple<T...>& x, std::integer_sequence<int, i...>)
{
   return tuple{a / get<i>(x)...};
}
 
/**
 * @brief A helper function for the / operator of tuples
 *
 * @tparam T the types stored in the tuple y
 * @tparam i The integer sequence to i
 * @param x tuple of values
 * @param a the constant denominator
 * @return the returned tuple ratio
 */
template <typename... T, int... i>
MFEM_HOST_DEVICE constexpr auto div_helper(const tuple<T...>& x,
                                           const real_t a, std::integer_sequence<int, i...>)
{
   return tuple{get<i>(x) / a...};
}
 
/**
 * @tparam T the types stored in the tuple x
 * @param a the numerator
 * @param x a tuple of denominator values
 * @brief return a tuple of values defined by division of a by the elements of x
 */
template <typename... T>
MFEM_HOST_DEVICE constexpr auto operator/(const real_t a, const tuple<T...>& x)
{
   return div_helper(a, x,
                     std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
}
 
/**
 * @tparam T the types stored in the tuple y
 * @param x a tuple of numerator values
 * @param a a denominator
 * @brief return a tuple of values defined by elementwise division of x by a
 */
template <typename... T>
MFEM_HOST_DEVICE constexpr auto operator/(const tuple<T...>& x, const real_t a)
{
   return div_helper(x, a,
                     std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
}
 
/**
 * @brief A helper function for the * operator of tuples
 *
 * @tparam S the types stored in the tuple x
 * @tparam T the types stored in the tuple y
 * @tparam i The integer sequence to i
 * @param x tuple of values
 * @param y tuple of values
 * @return the returned tuple product
 */
template <typename... S, typename... T, int... i>
MFEM_HOST_DEVICE constexpr auto mult_helper(const tuple<S...>& x,
                                            const tuple<T...>& y,
                                            std::integer_sequence<int, i...>)
{
   return tuple{get<i>(x) * get<i>(y)...};
}
 
/**
 * @tparam S the types stored in the tuple x
 * @tparam T the types stored in the tuple y
 * @param x a tuple of values
 * @param y a tuple of values
 * @brief return a tuple of values defined by elementwise multiplication of x and y
 */
template <typename... S, typename... T>
MFEM_HOST_DEVICE constexpr auto operator*(const tuple<S...>& x,
                                          const tuple<T...>& y)
{
   static_assert(sizeof...(S) == sizeof...(T));
   return mult_helper(x, y,
                      std::make_integer_sequence<int, static_cast<int>(sizeof...(S))>());
}
 
/**
 * @brief A helper function for the * operator of tuples
 *
 * @tparam T the types stored in the tuple y
 * @tparam i The integer sequence to i
 * @param x tuple of values
 * @param a a constant multiplier
 * @return the returned tuple product
 */
template <typename... T, int... i>
MFEM_HOST_DEVICE constexpr auto mult_helper(const real_t a,
                                            const tuple<T...>& x, std::integer_sequence<int, i...>)
{
   return tuple{a * get<i>(x)...};
}
 
/**
 * @brief A helper function for the * operator of tuples
 *
 * @tparam T the types stored in the tuple y
 * @tparam i The integer sequence to i
 * @param x tuple of values
 * @param a a constant multiplier
 * @return the returned tuple product
 */
template <typename... T, int... i>
MFEM_HOST_DEVICE constexpr auto mult_helper(const tuple<T...>& x,
                                            const real_t a, std::integer_sequence<int, i...>)
{
   return tuple{get<i>(x) * a...};
}
 
/**
 * @tparam T the types stored in the tuple
 * @param a a scaling factor
 * @param x the tuple object
 * @brief multiply each component of x by the value a on the left
 */
template <typename... T>
MFEM_HOST_DEVICE constexpr auto operator*(const real_t a, const tuple<T...>& x)
{
   return mult_helper(a, x,
                      std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
}
 
/**
 * @tparam T the types stored in the tuple
 * @param x the tuple object
 * @param a a scaling factor
 * @brief multiply each component of x by the value a on the right
 */
template <typename... T>
MFEM_HOST_DEVICE constexpr auto operator*(const tuple<T...>& x, const real_t a)
{
   return mult_helper(x, a,
                      std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
}
 
/**
 * @tparam T the types stored in the tuple
 * @tparam i a list of indices used to access each element of the tuple
 * @param out the ostream to write the output to
 * @param A the tuple of values
 * @brief helper used to implement printing a tuple of values
 */
template <typename... T, std::size_t... i>
auto& print_helper(std::ostream& out, const tuple<T...>& A,
                   std::integer_sequence<size_t, i...>)
{
   out << "tuple{";
   (..., (out << (i == 0 ? "" : ", ") << get<i>(A)));
   out << "}";
   return out;
}
 
/**
 * @tparam T the types stored in the tuple
 * @param out the ostream to write the output to
 * @param A the tuple of values
 * @brief print a tuple of values
 */
template <typename... T>
auto& operator<<(std::ostream& out, const tuple<T...>& A)
{
   return print_helper(out, A, std::make_integer_sequence<size_t, sizeof...(T)>());
}
 
/**
 * @brief A helper to apply a lambda to a tuple
 *
 * @tparam lambda The functor type
 * @tparam T The tuple types
 * @tparam i The integer sequence to i
 * @param f The functor to apply to the tuple
 * @param args The input tuple
 * @return The functor output
 */
template <typename lambda, typename... T, int... i>
MFEM_HOST_DEVICE auto apply_helper(lambda f, tuple<T...>& args,
                                   std::integer_sequence<int, i...>)
{
   return f(get<i>(args)...);
}
 
/**
 * @tparam lambda a callable type
 * @tparam T the types of arguments to be passed in to f
 * @param f the callable object
 * @param args a tuple of arguments
 * @brief a way of passing an n-tuple to a function that expects n separate arguments
 *
 *   e.g. foo(bar, baz) is equivalent to apply(foo, mfem::tuple(bar,baz));
 */
template <typename lambda, typename... T>
MFEM_HOST_DEVICE auto apply(lambda f, tuple<T...>& args)
{
   return apply_helper(f, std::move(args),
                       std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
}
 
/**
 * @overload
 */
template <typename lambda, typename... T, int... i>
MFEM_HOST_DEVICE auto apply_helper(lambda f, const tuple<T...>& args,
                                   std::integer_sequence<int, i...>)
{
   return f(get<i>(args)...);
}
 
/**
 * @tparam lambda a callable type
 * @tparam T the types of arguments to be passed in to f
 * @param f the callable object
 * @param args a tuple of arguments
 * @brief a way of passing an n-tuple to a function that expects n separate arguments
 *
 *   e.g. foo(bar, baz) is equivalent to apply(foo, mfem::tuple(bar,baz));
 */
template <typename lambda, typename... T>
MFEM_HOST_DEVICE auto apply(lambda f, const tuple<T...>& args)
{
   return apply_helper(f, std::move(args),
                       std::make_integer_sequence<int, static_cast<int>(sizeof...(T))>());
}
 
/**
 * @brief a struct used to determine the type at index I of a tuple
 *
 * @note see: https://en.cppreference.com/w/cpp/utility/tuple/tuple_element
 *
 * @tparam I the index of the desired type
 * @tparam T a tuple of different types
 */
template <size_t I, class T>
struct tuple_element;
 
// recursive case
/// @overload
template <size_t I, class Head, class... Tail>
struct tuple_element<I, tuple<Head, Tail...>> : tuple_element<I - 1,
                                              tuple<Tail...>>
{
};
 
// base case
/// @overload
template <class Head, class... Tail>
struct tuple_element<0, tuple<Head, Tail...>>
{
   using type = Head;  ///< the type at the specified index
};
 
/**
 * @brief Trait for checking if a type is a @p mfem::tuple
 */
template <typename T>
struct is_tuple : std::false_type
{
};
 
/// @overload
template <typename... T>
struct is_tuple<tuple<T...>> : std::true_type
{
};
 
/**
 * @brief Trait for checking if a type if a @p mfem::tuple containing only @p mfem::tuple
 */
template <typename T>
struct is_tuple_of_tuples : std::false_type
{
};
 
/**
 * @brief Trait for checking if a type if a @p mfem::tuple containing only @p mfem::tuple
 */
template <typename... T>
struct is_tuple_of_tuples<tuple<T...>>
{
   static constexpr bool value = (is_tuple<T>::value &&
                                  ...);  ///< true/false result of type check
};
 
/** @brief Auxiliary template function that merges (concatenates) two
    mfem::future::tuple types into a single std::tuple that is empty, i.e. it is
    value initialized. */
template <typename... T1s, typename... T2s>
constexpr auto merge_mfem_tuples_as_empty_std_tuple(
   const mfem::future::tuple<T1s...> &,
   const mfem::future::tuple<T2s...> &)
{
   return std::tuple<T1s..., T2s...> {};
}
 
}  // namespace mfem::future