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derived_dimension code split to a few smaller files

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Mateusz Pusz
2019-12-14 12:23:47 +01:00
parent b1b63e1b3a
commit 8d1eb4c415
8 changed files with 381 additions and 219 deletions
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60
src/include/units/bits/base_units_ratio.h Normal file
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// The MIT License (MIT)
//
// Copyright (c) 2018 Mateusz Pusz
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
#pragma once
#include <units/base_dimension.h>
#include <units/exp.h>
#include <units/ratio.h>
namespace units::detail {
template<Exponent E>
requires (E::den == 1 || E::den == 2) // TODO provide support for any den
struct exp_ratio {
using base_ratio = E::dimension::base_unit::ratio;
using positive_ratio = conditional<E::num * E::den < 0, ratio<base_ratio::den, base_ratio::num>, base_ratio>;
static constexpr std::int64_t N = E::num * E::den < 0 ? -E::num : E::num;
using pow = ratio_pow<positive_ratio, N>;
using type = conditional<E::den == 2, ratio_sqrt<pow>, pow>;
};
template<typename ExpList>
struct base_units_ratio_impl;
template<typename E, typename... Es>
struct base_units_ratio_impl<exp_list<E, Es...>> {
using type = ratio_multiply<typename exp_ratio<E>::type, typename base_units_ratio_impl<exp_list<Es...>>::type>;
};
template<typename E>
struct base_units_ratio_impl<exp_list<E>> {
using type = exp_ratio<E>::type;
};
/**
* @brief Calculates the common ratio of all the references of base units in the derived dimension
*/
template<typename D>
using base_units_ratio = base_units_ratio_impl<typename D::exponents>::type;
} // namespace units::detail

61
src/include/units/bits/derived_dimension_base.h Normal file
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// The MIT License (MIT)
//
// Copyright (c) 2018 Mateusz Pusz
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
#pragma once
#include <units/base_dimension.h>
#include <units/bits/external/downcasting.h>
#include <units/exp.h>
namespace units::detail {
/**
* @brief A dimension of a derived quantity
*
* Expression of the dependence of a quantity on the base quantities (and their base dimensions) of a system of
* quantities as a product of powers of factors corresponding to the base quantities, omitting any numerical factors.
* A power of a factor is the factor raised to an exponent.
*
* A derived dimension can be formed from multiple exponents (i.e. velocity is represented as "exp<L, 1>, exp<T, -1>").
* It is also possible to form a derived dimension with only one exponent (i.e. frequency is represented as just
* "exp<T, -1>").
*
* @note This class template is used by the library engine and should not be directly instantiated by the user.
*
* @tparam E a first exponent of a derived dimension
* @tparam ERest zero or more following exponents of a derived dimension
*/
template<Exponent E, Exponent... ERest>
requires (BaseDimension<typename E::dimension> && ... && BaseDimension<typename ERest::dimension>)
struct derived_dimension_base : downcast_base<derived_dimension_base<E, ERest...>> {
using exponents = exp_list<E, ERest...>;
};
template<typename T>
struct to_derived_dimension_base;
template<Exponent... Es>
struct to_derived_dimension_base<exp_list<Es...>> {
using type = derived_dimension_base<Es...>;
};
} // namespace units::detail

67
src/include/units/bits/dim_consolidate.h Normal file
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// The MIT License (MIT)
//
// Copyright (c) 2018 Mateusz Pusz
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
#pragma once
#include <units/bits/external/type_list.h>
#include <units/exp.h>
#include <ratio> // TODO remove this dependency with #11
namespace units::detail {
/**
* @brief Consolidates contiguous ranges of exponents of the same dimension
*
* If there is more than one exponent with the same dimension they are aggregated into one exponent by adding
* their exponents. If this accumulation will result with 0, such a dimension is removed from the list.
*
* @tparam D derived dimension to consolidate
*/
template<typename ExpList>
struct dim_consolidate;
template<>
struct dim_consolidate<exp_list<>> {
using type = exp_list<>;
};
template<typename E>
struct dim_consolidate<exp_list<E>> {
using type = exp_list<E>;
};
template<typename E1, typename... ERest>
struct dim_consolidate<exp_list<E1, ERest...>> {
using type = type_list_push_front<typename dim_consolidate<exp_list<ERest...>>::type, E1>;
};
template<BaseDimension Dim, int Num1, int Den1, int Num2, int Den2, typename... ERest>
struct dim_consolidate<exp_list<exp<Dim, Num1, Den1>, exp<Dim, Num2, Den2>, ERest...>> {
// TODO: provide custom implementation for ratio_add
using r1 = std::ratio<Num1, Den1>;
using r2 = std::ratio<Num2, Den2>;
using r = std::ratio_add<r1, r2>;
using type = conditional<r::num == 0, typename dim_consolidate<exp_list<ERest...>>::type,
typename dim_consolidate<exp_list<exp<Dim, r::num, r::den>, ERest...>>::type>;
};
} // namespace units::detail

59
src/include/units/bits/dim_unpack.h Normal file
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// The MIT License (MIT)
//
// Copyright (c) 2018 Mateusz Pusz
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
#pragma once
#include <units/bits/derived_dimension_base.h>
#include <units/bits/external/type_list.h>
#include <units/exp.h>
namespace units::detail {
/**
* @brief Unpacks the list of potentially derived dimensions to a list containing only base dimensions
*
* @tparam Es Exponents of potentially derived dimensions
*/
template<Exponent... Es>
struct dim_unpack;
template<>
struct dim_unpack<> {
using type = exp_list<>;
};
template<BaseDimension Dim, int Num, int Den, Exponent... ERest>
struct dim_unpack<exp<Dim, Num, Den>, ERest...> {
using type = type_list_push_front<typename dim_unpack<ERest...>::type, exp<Dim, Num, Den>>;
};
template<DerivedDimension Dim, int Num, int Den, Exponent... ERest>
struct dim_unpack<exp<Dim, Num, Den>, ERest...> {
using type = dim_unpack<exp<downcast_base_t<Dim>, Num, Den>, ERest...>::type;
};
template<Exponent... Es, int Num, int Den, Exponent... ERest>
struct dim_unpack<exp<derived_dimension_base<Es...>, Num, Den>, ERest...> {
using type = type_list_push_front<typename dim_unpack<ERest...>::type, exp_multiply<Es, Num, Den>...>;
};
} // namespace units::detail

6
src/include/units/concepts.h
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@@ -126,12 +126,16 @@ template<typename T>
concept Exponent = detail::is_exp<T>;
// DerivedDimension
namespace detail {
template<Exponent E, Exponent... ERest>
requires (BaseDimension<typename E::dimension> && ... && BaseDimension<typename ERest::dimension>)
struct derived_dimension_base;
} // namespace detail
template<typename T>
concept DerivedDimension = is_instantiation<downcast_base_t<T>, derived_dimension_base>;
concept DerivedDimension = is_instantiation<downcast_base_t<T>, detail::derived_dimension_base>;
// Dimension
template<typename T>

191
src/include/units/derived_dimension.h
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@@ -23,168 +23,18 @@
#pragma once
#include <units/base_dimension.h>
#include <units/bits/base_units_ratio.h>
#include <units/bits/derived_dimension_base.h>
#include <units/bits/dim_consolidate.h>
#include <units/bits/dim_unpack.h>
#include <units/bits/external/downcasting.h>
#include <units/bits/external/fixed_string.h>
#include <units/bits/external/type_list.h>
#include <units/ratio.h>
#include <ratio>
#include <units/exp.h>
namespace units {
/**
* @brief A power of factor corresponding to the dimension of a quantity
*
* @tparam Dim component dimension of a derived quantity
* @tparam Num numinator of the factor
* @tparam Den denominator of the factor
*/
template<Dimension Dim, int Num, int Den = 1>
struct exp {
using dimension = Dim;
static constexpr int num = Num;
static constexpr int den = Den;
};
// is_exp
namespace detail {
template<typename Dim, int Num, int Den>
inline constexpr bool is_exp<exp<Dim, Num, Den>> = true;
} // namespace detail
// exp_less
template<Exponent E1, Exponent E2>
struct exp_less : base_dimension_less<typename E1::dimension, typename E2::dimension> {};
// exp_invert
namespace detail {
template<typename Dim, int Num, int Den>
constexpr exp<Dim, -Num, Den> exp_invert_impl(exp<Dim, Num, Den>);
} // namespace detail
template<Exponent E>
using exp_invert = decltype(detail::exp_invert_impl(E()));
// exp_multiply
namespace detail {
template<Exponent E, int Num, int Den>
struct exp_multiply_impl {
using r1 = ratio<E::num, E::den>;
using r2 = ratio<Num, Den>;
using r = ratio_multiply<r1, r2>;
using type = exp<typename E::dimension, r::num, r::den>;
};
} // namespace detail
template<Exponent E, int Num, int Den>
using exp_multiply = detail::exp_multiply_impl<E, Num, Den>::type;
template<Exponent... Es>
struct exp_list {};
/**
* @brief A dimension of a derived quantity
*
* Expression of the dependence of a quantity on the base quantities (and their base dimensions) of a system of
* quantities as a product of powers of factors corresponding to the base quantities, omitting any numerical factors.
* A power of a factor is the factor raised to an exponent.
*
* A derived dimension can be formed from multiple exponents (i.e. velocity is represented as "exp<L, 1>, exp<T, -1>").
* It is also possible to form a derived dimension with only one exponent (i.e. frequency is represented as just
* "exp<T, -1>").
*
* @note This class template is used by the library engine and should not be directly instantiated by the user.
*
* @tparam E a first exponent of a derived dimension
* @tparam ERest zero or more following exponents of a derived dimension
*/
template<Exponent E, Exponent... ERest>
requires (BaseDimension<typename E::dimension> && ... && BaseDimension<typename ERest::dimension>)
struct derived_dimension_base : downcast_base<derived_dimension_base<E, ERest...>> {
using exponents = exp_list<E, ERest...>;
};
// make_dimension
namespace detail {
/**
* @brief Consolidates contiguous ranges of exponents of the same dimension
*
* If there is more than one exponent with the same dimension they are aggregated into one exponent by adding
* their exponents. If this accumulation will result with 0, such a dimension is removed from the list.
*
* @tparam D derived dimension to consolidate
*/
template<typename ExpList>
struct dim_consolidate;
template<>
struct dim_consolidate<exp_list<>> {
using type = exp_list<>;
};
template<typename E>
struct dim_consolidate<exp_list<E>> {
using type = exp_list<E>;
};
template<typename E1, typename... ERest>
struct dim_consolidate<exp_list<E1, ERest...>> {
using type = type_list_push_front<typename dim_consolidate<exp_list<ERest...>>::type, E1>;
};
template<BaseDimension Dim, int Num1, int Den1, int Num2, int Den2, typename... ERest>
struct dim_consolidate<exp_list<exp<Dim, Num1, Den1>, exp<Dim, Num2, Den2>, ERest...>> {
// TODO: provide custom implementation for ratio_add
using r1 = std::ratio<Num1, Den1>;
using r2 = std::ratio<Num2, Den2>;
using r = std::ratio_add<r1, r2>;
using type = conditional<r::num == 0, typename dim_consolidate<exp_list<ERest...>>::type,
typename dim_consolidate<exp_list<exp<Dim, r::num, r::den>, ERest...>>::type>;
};
/**
* @brief Extracts the list of potentially derived dimensions to a list containing only base dimensions
*
* @tparam Es Exponents of potentially derived dimensions
*/
template<Exponent... Es>
struct extract;
template<>
struct extract<> {
using type = exp_list<>;
};
template<BaseDimension Dim, int Num, int Den, Exponent... ERest>
struct extract<exp<Dim, Num, Den>, ERest...> {
using type = type_list_push_front<typename extract<ERest...>::type, exp<Dim, Num, Den>>;
};
template<DerivedDimension Dim, int Num, int Den, Exponent... ERest>
struct extract<exp<Dim, Num, Den>, ERest...> {
using type = extract<exp<downcast_base_t<Dim>, Num, Den>, ERest...>::type;
};
template<Exponent... Es, int Num, int Den, Exponent... ERest>
struct extract<exp<derived_dimension_base<Es...>, Num, Den>, ERest...> {
using type = type_list_push_front<typename extract<ERest...>::type, exp_multiply<Es, Num, Den>...>;
};
template<typename T>
struct to_derived_dimension_base;
template<Exponent... Es>
struct to_derived_dimension_base<exp_list<Es...>> {
using type = derived_dimension_base<Es...>;
};
/**
* @brief Converts user provided derived dimension specification into a valid units::derived_dimension_base definition
*
@@ -196,36 +46,7 @@ struct to_derived_dimension_base<exp_list<Es...>> {
* this base dimension.
*/
template<Exponent... Es>
using make_dimension = to_derived_dimension_base<typename dim_consolidate<type_list_sort<typename extract<Es...>::type, exp_less>>::type>::type;
template<Exponent E>
requires (E::den == 1 || E::den == 2) // TODO provide support for any den
struct exp_ratio {
using base_ratio = E::dimension::base_unit::ratio;
using positive_ratio = conditional<E::num * E::den < 0, ratio<base_ratio::den, base_ratio::num>, base_ratio>;
static constexpr std::int64_t N = E::num * E::den < 0 ? -E::num : E::num;
using pow = ratio_pow<positive_ratio, N>;
using type = conditional<E::den == 2, ratio_sqrt<pow>, pow>;
};
template<typename ExpList>
struct base_units_ratio_impl;
template<typename E, typename... Es>
struct base_units_ratio_impl<exp_list<E, Es...>> {
using type = ratio_multiply<typename exp_ratio<E>::type, typename base_units_ratio_impl<exp_list<Es...>>::type>;
};
template<typename E>
struct base_units_ratio_impl<exp_list<E>> {
using type = exp_ratio<E>::type;
};
/**
* @brief Calculates the common ratio of all the references of base units in the derived dimension
*/
template<typename D>
using base_units_ratio = base_units_ratio_impl<typename D::exponents>::type;
using make_dimension = to_derived_dimension_base<typename dim_consolidate<type_list_sort<typename dim_unpack<Es...>::type, exp_less>>::type>::type;
} // namespace detail

87
src/include/units/exp.h Normal file
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@@ -0,0 +1,87 @@
// The MIT License (MIT)
//
// Copyright (c) 2018 Mateusz Pusz
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in all
// copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
// SOFTWARE.
#pragma once
#include <units/base_dimension.h>
#include <units/ratio.h>
namespace units {
/**
* @brief A power of factor corresponding to the dimension of a quantity
*
* @tparam Dim component dimension of a derived quantity
* @tparam Num numinator of the factor
* @tparam Den denominator of the factor
*/
template<Dimension Dim, int Num, int Den = 1>
struct exp {
using dimension = Dim;
static constexpr int num = Num;
static constexpr int den = Den;
};
// is_exp
namespace detail {
template<typename Dim, int Num, int Den>
inline constexpr bool is_exp<exp<Dim, Num, Den>> = true;
} // namespace detail
// exp_less
template<Exponent E1, Exponent E2>
requires BaseDimension<typename E1::dimension> && BaseDimension<typename E2::dimension>
struct exp_less : base_dimension_less<typename E1::dimension, typename E2::dimension> {};
// exp_invert
namespace detail {
template<typename Dim, int Num, int Den>
constexpr exp<Dim, -Num, Den> exp_invert_impl(exp<Dim, Num, Den>);
} // namespace detail
template<Exponent E>
using exp_invert = decltype(detail::exp_invert_impl(E()));
// exp_multiply
namespace detail {
template<Exponent E, int Num, int Den>
struct exp_multiply_impl {
using r1 = ratio<E::num, E::den>;
using r2 = ratio<Num, Den>;
using r = ratio_multiply<r1, r2>;
using type = exp<typename E::dimension, r::num, r::den>;
};
} // namespace detail
template<Exponent E, int Num, int Den>
using exp_multiply = detail::exp_multiply_impl<E, Num, Den>::type;
template<Exponent... Es>
struct exp_list {};
} // namespace units

69
test/unit_test/static/dimension_op_test.cpp
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@@ -42,75 +42,78 @@ struct d3 : base_dimension<"d3", u3> {};
static_assert(std::is_same_v<exp_invert<exp<d0, 2>>, exp<d0, -2>>);
static_assert(std::is_same_v<exp_invert<exp<d1, -2>>, exp<d1, 2>>);
// extract
// dim_unpack
template<typename T>
struct typeinfo;
template<typename... Ts>
using extract = detail::extract<Ts...>::type;
using dim_unpack = detail::dim_unpack<Ts...>::type;
static_assert(std::is_same_v<extract<>, exp_list<>>);
static_assert(std::is_same_v<extract<exp<d0, 1>>, exp_list<exp<d0, 1>>>);
static_assert(std::is_same_v<extract<exp<d0, 1>, exp<d1, 2>>, exp_list<exp<d0, 1>, exp<d1, 2>>>);
using dim1 = derived_dimension_base<exp<d0, 1>>;
using dim2 = derived_dimension_base<exp<d0, 1>, exp<d1, 2>>;
static_assert(std::is_same_v<extract<exp<dim1, 2>, exp<d0, 1>>, exp_list<exp<d0, 2>, exp<d0, 1>>>);
static_assert(std::is_same_v<extract<exp<dim2, -2>, exp<d0, 1>, exp<d1, 2>>,
template<Exponent... Es>
using derived_dim = detail::derived_dimension_base<Es...>;
static_assert(std::is_same_v<dim_unpack<>, exp_list<>>);
static_assert(std::is_same_v<dim_unpack<exp<d0, 1>>, exp_list<exp<d0, 1>>>);
static_assert(std::is_same_v<dim_unpack<exp<d0, 1>, exp<d1, 2>>, exp_list<exp<d0, 1>, exp<d1, 2>>>);
using dim1 = derived_dim<exp<d0, 1>>;
using dim2 = derived_dim<exp<d0, 1>, exp<d1, 2>>;
static_assert(std::is_same_v<dim_unpack<exp<dim1, 2>, exp<d0, 1>>, exp_list<exp<d0, 2>, exp<d0, 1>>>);
static_assert(std::is_same_v<dim_unpack<exp<dim2, -2>, exp<d0, 1>, exp<d1, 2>>,
exp_list<exp<d0, -2>, exp<d1, -4>, exp<d0, 1>, exp<d1, 2>>>);
// dim_invert
static_assert(std::is_same_v<dim_invert<derived_dimension_base<exp<d0, -1>>>, d0>);
static_assert(std::is_same_v<dim_invert<derived_dimension_base<exp<d0, -2>>>, unknown_dimension<exp<d0, 2>>>);
static_assert(std::is_same_v<dim_invert<derived_dim<exp<d0, -1>>>, d0>);
static_assert(std::is_same_v<dim_invert<derived_dim<exp<d0, -2>>>, unknown_dimension<exp<d0, 2>>>);
static_assert(
std::is_same_v<dim_invert<derived_dimension_base<exp<d0, 2>, exp<d1, -1>>>, unknown_dimension<exp<d0, -2>, exp<d1, 1>>>);
std::is_same_v<dim_invert<derived_dim<exp<d0, 2>, exp<d1, -1>>>, unknown_dimension<exp<d0, -2>, exp<d1, 1>>>);
// make_dimension
template<typename... Ts>
using make_dimension = detail::make_dimension<Ts...>;
static_assert(std::is_same_v<make_dimension<exp<d0, 1>>, derived_dimension_base<exp<d0, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>, exp<d1, 1>>, derived_dimension_base<exp<d0, 1>, exp<d1, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 1>, exp<d0, 1>>, derived_dimension_base<exp<d0, 1>, exp<d1, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 1>, exp<d1, 1>>, derived_dimension_base<exp<d1, 2>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 1>, exp<d1, 1, 2>>, derived_dimension_base<exp<d1, 3, 2>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 1, 2>, exp<d1, 1, 2>>, derived_dimension_base<exp<d1, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 2>, exp<d1, 1, 2>>, derived_dimension_base<exp<d1, 5, 2>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>>, derived_dim<exp<d0, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>, exp<d1, 1>>, derived_dim<exp<d0, 1>, exp<d1, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 1>, exp<d0, 1>>, derived_dim<exp<d0, 1>, exp<d1, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 1>, exp<d1, 1>>, derived_dim<exp<d1, 2>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 1>, exp<d1, 1, 2>>, derived_dim<exp<d1, 3, 2>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 1, 2>, exp<d1, 1, 2>>, derived_dim<exp<d1, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d1, 2>, exp<d1, 1, 2>>, derived_dim<exp<d1, 5, 2>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>, exp<d1, 1>, exp<d0, 1>, exp<d1, 1>>,
derived_dimension_base<exp<d0, 2>, exp<d1, 2>>>);
derived_dim<exp<d0, 2>, exp<d1, 2>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, -1>, exp<d1, -1>, exp<d0, -1>, exp<d1, -1>>,
derived_dimension_base<exp<d0, -2>, exp<d1, -2>>>);
derived_dim<exp<d0, -2>, exp<d1, -2>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>, exp<d1, 1>, exp<d1, -1>>, derived_dimension_base<exp<d0, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>, exp<d0, -1>, exp<d1, 1>>, derived_dimension_base<exp<d1, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>, exp<d1, 1>, exp<d0, -1>>, derived_dimension_base<exp<d1, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>, exp<d1, 1>, exp<d1, -1>>, derived_dim<exp<d0, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>, exp<d0, -1>, exp<d1, 1>>, derived_dim<exp<d1, 1>>>);
static_assert(std::is_same_v<make_dimension<exp<d0, 1>, exp<d1, 1>, exp<d0, -1>>, derived_dim<exp<d1, 1>>>);
// dimension_multiply
static_assert(std::is_same_v<dimension_multiply<derived_dimension_base<exp<d0, 1>>, derived_dimension_base<exp<d1, 1>>>,
static_assert(std::is_same_v<dimension_multiply<derived_dim<exp<d0, 1>>, derived_dim<exp<d1, 1>>>,
unknown_dimension<exp<d0, 1>, exp<d1, 1>>>);
static_assert(
std::is_same_v<dimension_multiply<derived_dimension_base<exp<d0, 1>>, d1>, unknown_dimension<exp<d0, 1>, exp<d1, 1>>>);
std::is_same_v<dimension_multiply<derived_dim<exp<d0, 1>>, d1>, unknown_dimension<exp<d0, 1>, exp<d1, 1>>>);
static_assert(
std::is_same_v<dimension_multiply<d0, derived_dimension_base<exp<d1, 1>>>, unknown_dimension<exp<d0, 1>, exp<d1, 1>>>);
std::is_same_v<dimension_multiply<d0, derived_dim<exp<d1, 1>>>, unknown_dimension<exp<d0, 1>, exp<d1, 1>>>);
static_assert(std::is_same_v<dimension_multiply<d0, d1>, unknown_dimension<exp<d0, 1>, exp<d1, 1>>>);
static_assert(std::is_same_v<
dimension_multiply<derived_dimension_base<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>>, derived_dimension_base<exp<d3, 1>>>,
dimension_multiply<derived_dim<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>>, derived_dim<exp<d3, 1>>>,
unknown_dimension<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>, exp<d3, 1>>>);
static_assert(std::is_same_v<
dimension_multiply<derived_dimension_base<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>>, derived_dimension_base<exp<d1, 1>>>,
dimension_multiply<derived_dim<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>>, derived_dim<exp<d1, 1>>>,
unknown_dimension<exp<d0, 1>, exp<d1, 2>, exp<d2, 1>>>);
static_assert(std::is_same_v<
dimension_multiply<derived_dimension_base<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>>, derived_dimension_base<exp<d1, -1>>>,
dimension_multiply<derived_dim<exp<d0, 1>, exp<d1, 1>, exp<d2, 1>>, derived_dim<exp<d1, -1>>>,
unknown_dimension<exp<d0, 1>, exp<d2, 1>>>);
static_assert(std::is_same_v<dimension_multiply<derived_dimension_base<exp<d0, 2>>, derived_dimension_base<exp<d0, -1>>>, d0>);
static_assert(std::is_same_v<dimension_multiply<derived_dim<exp<d0, 2>>, derived_dim<exp<d0, -1>>>, d0>);
// dimension_divide
static_assert(std::is_same_v<dimension_divide<derived_dimension_base<exp<d0, 1>>, derived_dimension_base<exp<d1, 1>>>,
static_assert(std::is_same_v<dimension_divide<derived_dim<exp<d0, 1>>, derived_dim<exp<d1, 1>>>,
unknown_dimension<exp<d0, 1>, exp<d1, -1>>>);
static_assert(std::is_same_v<dimension_divide<derived_dimension_base<exp<d0, 2>>, unknown_dimension<exp<d0, 1>>>, d0>);
static_assert(std::is_same_v<dimension_divide<derived_dim<exp<d0, 2>>, unknown_dimension<exp<d0, 1>>>, d0>);
} // namespace