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units.h
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units.h
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//--------------------------------------------------------------------------------------------------
//
// Units: A compile-time c++14 unit conversion library with no dependencies
//
//--------------------------------------------------------------------------------------------------
//
// The MIT License (MIT)
//
// 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.
//
//--------------------------------------------------------------------------------------------------
//
// Copyright (c) 2016 Nic Holthaus
//
//--------------------------------------------------------------------------------------------------
//
// ATTRIBUTION:
// Parts of this work have been adapted from:
// http://stackoverflow.com/questions/35069778/create-comparison-trait-for-template-classes-whose-parameters-are-in-a-different
// http://stackoverflow.com/questions/28253399/check-traits-for-all-variadic-template-arguments/28253503
// http://stackoverflow.com/questions/36321295/rational-approximation-of-square-root-of-stdratio-at-compile-time?noredirect=1#comment60266601_36321295
//
//--------------------------------------------------------------------------------------------------
//
/// @file units.h
/// @brief Complete implementation of `units` - a compile-time, header-only, unit conversion
/// library built on c++14 with no dependencies.
//
//--------------------------------------------------------------------------------------------------
#pragma once
#ifndef units_h__
#define units_h__
#ifdef _MSC_VER
# pragma push_macro("pascal")
# undef pascal
# if _MSC_VER <= 1800
# define _ALLOW_KEYWORD_MACROS
# pragma warning(push)
# pragma warning(disable : 4520)
# pragma push_macro("constexpr")
# define constexpr /*constexpr*/
# pragma push_macro("noexcept")
# define noexcept throw()
# endif // _MSC_VER < 1800
#endif // _MSC_VER
#if defined(__MINGW64__) || defined(__MINGW32__)
# pragma push_macro("pascal")
# undef pascal
#endif // __MINGW64__ or __MINGW32__
#if !defined(_MSC_VER) || _MSC_VER > 1800
# define UNIT_HAS_LITERAL_SUPPORT
# define UNIT_HAS_VARIADIC_TEMPLATE_SUPPORT
#endif
#ifndef UNIT_LIB_DEFAULT_TYPE
# define UNIT_LIB_DEFAULT_TYPE double
#endif
//--------------------
// INCLUDES
//--------------------
#include <chrono>
#include <cstddef>
#include <ratio>
#include <type_traits>
#include <cstdint>
#include <cmath>
#include <limits>
#if !defined(UNIT_LIB_DISABLE_IOSTREAM)
#include <iostream>
#include <string>
#include <locale>
//------------------------------
// STRING FORMATTER
//------------------------------
namespace units
{
namespace detail
{
template <typename T> std::string to_string(const T& t)
{
std::string str{ std::to_string(t) };
int offset{ 1 };
// remove trailing decimal points for integer value units. Locale aware!
struct lconv * lc;
lc = localeconv();
char decimalPoint = *lc->decimal_point;
if (str.find_last_not_of('0') == str.find(decimalPoint)) { offset = 0; }
str.erase(str.find_last_not_of('0') + offset, std::string::npos);
return str;
}
}
}
#endif
namespace units
{
template<typename T> inline constexpr const char* name(const T&);
template<typename T> inline constexpr const char* name_plural(const T&);
template<typename T> inline constexpr const char* abbreviation(const T&);
}
//------------------------------
// MACROS
//------------------------------
/**
* @def UNIT_ADD_UNIT_TAGS(namespaceName,nameSingular, namePlural, abbreviation, definition)
* @brief Helper macro for generating the boiler-plate code generating the tags of a new unit.
* @details The macro generates singular, plural, and abbreviated forms
* of the unit definition (e.g. `meter`, `meters`, and `m`), as aliases for the
* unit tag.
* @param namespaceName namespace in which the new units will be encapsulated.
* @param nameSingular singular version of the unit name, e.g. 'meter'
* @param namePlural - plural version of the unit name, e.g. 'meters'
* @param abbreviation - abbreviated unit name, e.g. 'm'
* @param definition - the variadic parameter is used for the definition of the unit
* (e.g. `unit<std::ratio<1>, units::category::length_unit>`)
* @note a variadic template is used for the definition to allow templates with
* commas to be easily expanded. All the variadic 'arguments' should together
* comprise the unit definition.
*/
#define UNIT_ADD_UNIT_TAGS(namespaceName,nameSingular, namePlural, abbreviation, /*definition*/...)\
namespace namespaceName\
{\
/** @name Units (full names plural) */ /** @{ */ typedef __VA_ARGS__ namePlural; /** @} */\
/** @name Units (full names singular) */ /** @{ */ typedef namePlural nameSingular; /** @} */\
/** @name Units (abbreviated) */ /** @{ */ typedef namePlural abbreviation; /** @} */\
}
/**
* @def UNIT_ADD_UNIT_DEFINITION(namespaceName,nameSingular)
* @brief Macro for generating the boiler-plate code for the unit_t type definition.
* @details The macro generates the definition of the unit container types, e.g. `meter_t`
* @param namespaceName namespace in which the new units will be encapsulated.
* @param nameSingular singular version of the unit name, e.g. 'meter'
*/
#define UNIT_ADD_UNIT_DEFINITION(namespaceName,nameSingular)\
namespace namespaceName\
{\
/** @name Unit Containers */ /** @{ */ typedef unit_t<nameSingular> nameSingular ## _t; /** @} */\
}
/**
* @def UNIT_ADD_CUSTOM_TYPE_UNIT_DEFINITION(namespaceName,nameSingular,underlyingType)
* @brief Macro for generating the boiler-plate code for a unit_t type definition with a non-default underlying type.
* @details The macro generates the definition of the unit container types, e.g. `meter_t`
* @param namespaceName namespace in which the new units will be encapsulated.
* @param nameSingular singular version of the unit name, e.g. 'meter'
* @param underlyingType the underlying type
*/
#define UNIT_ADD_CUSTOM_TYPE_UNIT_DEFINITION(namespaceName,nameSingular, underlyingType)\
namespace namespaceName\
{\
/** @name Unit Containers */ /** @{ */ typedef unit_t<nameSingular,underlyingType> nameSingular ## _t; /** @} */\
}
/**
* @def UNIT_ADD_IO(namespaceName,nameSingular, abbreviation)
* @brief Macro for generating the boiler-plate code needed for I/O for a new unit.
* @details The macro generates the code to insert units into an ostream. It
* prints both the value and abbreviation of the unit when invoked.
* @param namespaceName namespace in which the new units will be encapsulated.
* @param nameSingular singular version of the unit name, e.g. 'meter'
* @param abbrev - abbreviated unit name, e.g. 'm'
* @note When UNIT_LIB_DISABLE_IOSTREAM is defined, the macro does not generate any code
*/
#if defined(UNIT_LIB_DISABLE_IOSTREAM)
#define UNIT_ADD_IO(namespaceName, nameSingular, abbrev)
#else
#define UNIT_ADD_IO(namespaceName, nameSingular, abbrev)\
namespace namespaceName\
{\
inline std::ostream& operator<<(std::ostream& os, const nameSingular ## _t& obj) \
{\
os << obj() << " "#abbrev; return os; \
}\
inline std::string to_string(const nameSingular ## _t& obj)\
{\
return units::detail::to_string(obj()) + std::string(" "#abbrev);\
}\
}
#endif
/**
* @def UNIT_ADD_NAME(namespaceName,nameSingular,namePlural,abbreviation)
* @brief Macro for generating constexpr names/abbreviations for units.
* @details The macro generates names for units. E.g. name() of 1_m would be "meter", and
* abbreviation would be "m".
* @param namespaceName namespace in which the new units will be encapsulated. All literal values
* are placed in the `units::literals` namespace.
* @param nameSingular singular version of the unit name, e.g. 'meter'
* @param namePlural plural version of the unit name, e.g. 'meters'
* @param abbreviation - abbreviated unit name, e.g. 'm'
*/
#define UNIT_ADD_NAME(namespaceName, nameSingular, namePlural, abbrev)\
template<> inline constexpr const char* name(const namespaceName::nameSingular ## _t&)\
{\
return #nameSingular;\
}\
template<> inline constexpr const char* abbreviation(const namespaceName::nameSingular ## _t&)\
{\
return #abbrev;\
}\
template<> inline constexpr const char* name_plural(const namespaceName::nameSingular ## _t&)\
{\
return #namePlural;\
}
/**
* @def UNIT_ADD_LITERALS(namespaceName,nameSingular,abbreviation)
* @brief Macro for generating user-defined literals for units.
* @details The macro generates user-defined literals for units. A literal suffix is created
* using the abbreviation (e.g. `10.0_m`).
* @param namespaceName namespace in which the new units will be encapsulated. All literal values
* are placed in the `units::literals` namespace.
* @param nameSingular singular version of the unit name, e.g. 'meter'
* @param abbreviation - abbreviated unit name, e.g. 'm'
* @note When UNIT_HAS_LITERAL_SUPPORT is not defined, the macro does not generate any code
*/
#if defined(UNIT_HAS_LITERAL_SUPPORT)
#define UNIT_ADD_LITERALS(namespaceName, nameSingular, abbreviation)\
namespace literals\
{\
inline constexpr namespaceName::nameSingular ## _t operator""_ ## abbreviation(long double d)\
{\
return namespaceName::nameSingular ## _t(static_cast<namespaceName::nameSingular ## _t::underlying_type>(d));\
}\
inline constexpr namespaceName::nameSingular ## _t operator""_ ## abbreviation (unsigned long long d)\
{\
return namespaceName::nameSingular ## _t(static_cast<namespaceName::nameSingular ## _t::underlying_type>(d));\
}\
}
#else
#define UNIT_ADD_LITERALS(namespaceName, nameSingular, abbreviation)
#endif
/**
* @def UNIT_ADD(namespaceName,nameSingular, namePlural, abbreviation, definition)
* @brief Macro for generating the boiler-plate code needed for a new unit.
* @details The macro generates singular, plural, and abbreviated forms
* of the unit definition (e.g. `meter`, `meters`, and `m`), as well as the
* appropriately named unit container (e.g. `meter_t`). A literal suffix is created
* using the abbreviation (e.g. `10.0_m`). It also defines a class-specific
* cout function which prints both the value and abbreviation of the unit when invoked.
* @param namespaceName namespace in which the new units will be encapsulated. All literal values
* are placed in the `units::literals` namespace.
* @param nameSingular singular version of the unit name, e.g. 'meter'
* @param namePlural - plural version of the unit name, e.g. 'meters'
* @param abbreviation - abbreviated unit name, e.g. 'm'
* @param definition - the variadic parameter is used for the definition of the unit
* (e.g. `unit<std::ratio<1>, units::category::length_unit>`)
* @note a variadic template is used for the definition to allow templates with
* commas to be easily expanded. All the variadic 'arguments' should together
* comprise the unit definition.
*/
#define UNIT_ADD(namespaceName, nameSingular, namePlural, abbreviation, /*definition*/...)\
UNIT_ADD_UNIT_TAGS(namespaceName,nameSingular, namePlural, abbreviation, __VA_ARGS__)\
UNIT_ADD_UNIT_DEFINITION(namespaceName,nameSingular)\
UNIT_ADD_NAME(namespaceName,nameSingular,namePlural, abbreviation)\
UNIT_ADD_IO(namespaceName,nameSingular, abbreviation)\
UNIT_ADD_LITERALS(namespaceName,nameSingular, abbreviation)
/**
* @def UNIT_ADD_WITH_CUSTOM_TYPE(namespaceName,nameSingular, namePlural, abbreviation, underlyingType, definition)
* @brief Macro for generating the boiler-plate code needed for a new unit with a non-default underlying type.
* @details The macro generates singular, plural, and abbreviated forms
* of the unit definition (e.g. `meter`, `meters`, and `m`), as well as the
* appropriately named unit container (e.g. `meter_t`). A literal suffix is created
* using the abbreviation (e.g. `10.0_m`). It also defines a class-specific
* cout function which prints both the value and abbreviation of the unit when invoked.
* @param namespaceName namespace in which the new units will be encapsulated. All literal values
* are placed in the `units::literals` namespace.
* @param nameSingular singular version of the unit name, e.g. 'meter'
* @param namePlural - plural version of the unit name, e.g. 'meters'
* @param abbreviation - abbreviated unit name, e.g. 'm'
* @param underlyingType - the underlying type, e.g. 'int' or 'float'
* @param definition - the variadic parameter is used for the definition of the unit
* (e.g. `unit<std::ratio<1>, units::category::length_unit>`)
* @note a variadic template is used for the definition to allow templates with
* commas to be easily expanded. All the variadic 'arguments' should together
* comprise the unit definition.
*/
#define UNIT_ADD_WITH_CUSTOM_TYPE(namespaceName, nameSingular, namePlural, abbreviation, underlyingType, /*definition*/...)\
UNIT_ADD_UNIT_TAGS(namespaceName,nameSingular, namePlural, abbreviation, __VA_ARGS__)\
UNIT_ADD_CUSTOM_TYPE_UNIT_DEFINITION(namespaceName,nameSingular,underlyingType)\
UNIT_ADD_IO(namespaceName,nameSingular, abbreviation)\
UNIT_ADD_LITERALS(namespaceName,nameSingular, abbreviation)
/**
* @def UNIT_ADD_DECIBEL(namespaceName, nameSingular, abbreviation)
* @brief Macro to create decibel container and literals for an existing unit type.
* @details This macro generates the decibel unit container, cout overload, and literal definitions.
* @param namespaceName namespace in which the new units will be encapsulated. All literal values
* are placed in the `units::literals` namespace.
* @param nameSingular singular version of the base unit name, e.g. 'watt'
* @param abbreviation - abbreviated decibel unit name, e.g. 'dBW'
*/
#define UNIT_ADD_DECIBEL(namespaceName, nameSingular, abbreviation)\
namespace namespaceName\
{\
/** @name Unit Containers */ /** @{ */ typedef unit_t<nameSingular, UNIT_LIB_DEFAULT_TYPE, units::decibel_scale> abbreviation ## _t; /** @} */\
}\
UNIT_ADD_IO(namespaceName, abbreviation, abbreviation)\
UNIT_ADD_LITERALS(namespaceName, abbreviation, abbreviation)
/**
* @def UNIT_ADD_CATEGORY_TRAIT(unitCategory, baseUnit)
* @brief Macro to create the `is_category_unit` type trait.
* @details This trait allows users to test whether a given type matches
* an intended category. This macro comprises all the boiler-plate
* code necessary to do so.
* @param unitCategory The name of the category of unit, e.g. length or mass.
*/
#define UNIT_ADD_CATEGORY_TRAIT_DETAIL(unitCategory)\
namespace traits\
{\
/** @cond */\
namespace detail\
{\
template<typename T> struct is_ ## unitCategory ## _unit_impl : std::false_type {};\
template<typename C, typename U, typename P, typename T>\
struct is_ ## unitCategory ## _unit_impl<units::unit<C, U, P, T>> : std::is_same<units::traits::base_unit_of<typename units::traits::unit_traits<units::unit<C, U, P, T>>::base_unit_type>, units::category::unitCategory ## _unit>::type {};\
template<typename U, typename S, template<typename> class N>\
struct is_ ## unitCategory ## _unit_impl<units::unit_t<U, S, N>> : std::is_same<units::traits::base_unit_of<typename units::traits::unit_t_traits<units::unit_t<U, S, N>>::unit_type>, units::category::unitCategory ## _unit>::type {};\
}\
/** @endcond */\
}
#if defined(UNIT_HAS_VARIADIC_TEMPLATE_SUPPORT)
#define UNIT_ADD_IS_UNIT_CATEGORY_TRAIT(unitCategory)\
namespace traits\
{\
template<typename... T> struct is_ ## unitCategory ## _unit : std::integral_constant<bool, units::all_true<units::traits::detail::is_ ## unitCategory ## _unit_impl<std::decay_t<T>>::value...>::value> {};\
}
#else
#define UNIT_ADD_IS_UNIT_CATEGORY_TRAIT(unitCategory)\
namespace traits\
{\
template<typename T1, typename T2 = T1, typename T3 = T1>\
struct is_ ## unitCategory ## _unit : std::integral_constant<bool, units::traits::detail::is_ ## unitCategory ## _unit_impl<typename std::decay<T1>::type>::value &&\
units::traits::detail::is_ ## unitCategory ## _unit_impl<typename std::decay<T2>::type>::value &&\
units::traits::detail::is_ ## unitCategory ## _unit_impl<typename std::decay<T3>::type>::value>{};\
}
#endif
#define UNIT_ADD_CATEGORY_TRAIT(unitCategory)\
UNIT_ADD_CATEGORY_TRAIT_DETAIL(unitCategory)\
/** @ingroup TypeTraits*/\
/** @brief Trait which tests whether a type represents a unit of unitCategory*/\
/** @details Inherits from `std::true_type` or `std::false_type`. Use `is_ ## unitCategory ## _unit<T>::value` to test the unit represents a unitCategory quantity.*/\
/** @tparam T one or more types to test*/\
UNIT_ADD_IS_UNIT_CATEGORY_TRAIT(unitCategory)
/**
* @def UNIT_ADD_WITH_METRIC_PREFIXES(nameSingular, namePlural, abbreviation, definition)
* @brief Macro for generating the boiler-plate code needed for a new unit, including its metric
* prefixes from femto to peta.
* @details See UNIT_ADD. In addition to generating the unit definition and containers '(e.g. `meters` and 'meter_t',
* it also creates corresponding units with metric suffixes such as `millimeters`, and `millimeter_t`), as well as the
* literal suffixes (e.g. `10.0_mm`).
* @param namespaceName namespace in which the new units will be encapsulated. All literal values
* are placed in the `units::literals` namespace.
* @param nameSingular singular version of the unit name, e.g. 'meter'
* @param namePlural - plural version of the unit name, e.g. 'meters'
* @param abbreviation - abbreviated unit name, e.g. 'm'
* @param definition - the variadic parameter is used for the definition of the unit
* (e.g. `unit<std::ratio<1>, units::category::length_unit>`)
* @note a variadic template is used for the definition to allow templates with
* commas to be easily expanded. All the variadic 'arguments' should together
* comprise the unit definition.
*/
#define UNIT_ADD_WITH_METRIC_PREFIXES(namespaceName, nameSingular, namePlural, abbreviation, /*definition*/...)\
UNIT_ADD(namespaceName, nameSingular, namePlural, abbreviation, __VA_ARGS__)\
UNIT_ADD(namespaceName, femto ## nameSingular, femto ## namePlural, f ## abbreviation, femto<namePlural>)\
UNIT_ADD(namespaceName, pico ## nameSingular, pico ## namePlural, p ## abbreviation, pico<namePlural>)\
UNIT_ADD(namespaceName, nano ## nameSingular, nano ## namePlural, n ## abbreviation, nano<namePlural>)\
UNIT_ADD(namespaceName, micro ## nameSingular, micro ## namePlural, u ## abbreviation, micro<namePlural>)\
UNIT_ADD(namespaceName, milli ## nameSingular, milli ## namePlural, m ## abbreviation, milli<namePlural>)\
UNIT_ADD(namespaceName, centi ## nameSingular, centi ## namePlural, c ## abbreviation, centi<namePlural>)\
UNIT_ADD(namespaceName, deci ## nameSingular, deci ## namePlural, d ## abbreviation, deci<namePlural>)\
UNIT_ADD(namespaceName, deca ## nameSingular, deca ## namePlural, da ## abbreviation, deca<namePlural>)\
UNIT_ADD(namespaceName, hecto ## nameSingular, hecto ## namePlural, h ## abbreviation, hecto<namePlural>)\
UNIT_ADD(namespaceName, kilo ## nameSingular, kilo ## namePlural, k ## abbreviation, kilo<namePlural>)\
UNIT_ADD(namespaceName, mega ## nameSingular, mega ## namePlural, M ## abbreviation, mega<namePlural>)\
UNIT_ADD(namespaceName, giga ## nameSingular, giga ## namePlural, G ## abbreviation, giga<namePlural>)\
UNIT_ADD(namespaceName, tera ## nameSingular, tera ## namePlural, T ## abbreviation, tera<namePlural>)\
UNIT_ADD(namespaceName, peta ## nameSingular, peta ## namePlural, P ## abbreviation, peta<namePlural>)\
/**
* @def UNIT_ADD_WITH_METRIC_AND_BINARY_PREFIXES(nameSingular, namePlural, abbreviation, definition)
* @brief Macro for generating the boiler-plate code needed for a new unit, including its metric
* prefixes from femto to peta, and binary prefixes from kibi to exbi.
* @details See UNIT_ADD. In addition to generating the unit definition and containers '(e.g. `bytes` and 'byte_t',
* it also creates corresponding units with metric suffixes such as `millimeters`, and `millimeter_t`), as well as the
* literal suffixes (e.g. `10.0_B`).
* @param namespaceName namespace in which the new units will be encapsulated. All literal values
* are placed in the `units::literals` namespace.
* @param nameSingular singular version of the unit name, e.g. 'byte'
* @param namePlural - plural version of the unit name, e.g. 'bytes'
* @param abbreviation - abbreviated unit name, e.g. 'B'
* @param definition - the variadic parameter is used for the definition of the unit
* (e.g. `unit<std::ratio<1>, units::category::data_unit>`)
* @note a variadic template is used for the definition to allow templates with
* commas to be easily expanded. All the variadic 'arguments' should together
* comprise the unit definition.
*/
#define UNIT_ADD_WITH_METRIC_AND_BINARY_PREFIXES(namespaceName, nameSingular, namePlural, abbreviation, /*definition*/...)\
UNIT_ADD_WITH_METRIC_PREFIXES(namespaceName, nameSingular, namePlural, abbreviation, __VA_ARGS__)\
UNIT_ADD(namespaceName, kibi ## nameSingular, kibi ## namePlural, Ki ## abbreviation, kibi<namePlural>)\
UNIT_ADD(namespaceName, mebi ## nameSingular, mebi ## namePlural, Mi ## abbreviation, mebi<namePlural>)\
UNIT_ADD(namespaceName, gibi ## nameSingular, gibi ## namePlural, Gi ## abbreviation, gibi<namePlural>)\
UNIT_ADD(namespaceName, tebi ## nameSingular, tebi ## namePlural, Ti ## abbreviation, tebi<namePlural>)\
UNIT_ADD(namespaceName, pebi ## nameSingular, pebi ## namePlural, Pi ## abbreviation, pebi<namePlural>)\
UNIT_ADD(namespaceName, exbi ## nameSingular, exbi ## namePlural, Ei ## abbreviation, exbi<namePlural>)
//--------------------
// UNITS NAMESPACE
//--------------------
/**
* @namespace units
* @brief Unit Conversion Library namespace
*/
namespace units
{
//----------------------------------
// DOXYGEN
//----------------------------------
/**
* @defgroup UnitContainers Unit Containers
* @brief Defines a series of classes which contain dimensioned values. Unit containers
* store a value, and support various arithmetic operations.
*/
/**
* @defgroup UnitTypes Unit Types
* @brief Defines a series of classes which represent units. These types are tags used by
* the conversion function, to create compound units, or to create `unit_t` types.
* By themselves, they are not containers and have no stored value.
*/
/**
* @defgroup UnitManipulators Unit Manipulators
* @brief Defines a series of classes used to manipulate unit types, such as `inverse<>`, `squared<>`, and metric prefixes.
* Unit manipulators can be chained together, e.g. `inverse<squared<pico<time::seconds>>>` to
* represent picoseconds^-2.
*/
/**
* @defgroup CompileTimeUnitManipulators Compile-time Unit Manipulators
* @brief Defines a series of classes used to manipulate `unit_value_t` types at compile-time, such as `unit_value_add<>`, `unit_value_sqrt<>`, etc.
* Compile-time manipulators can be chained together, e.g. `unit_value_sqrt<unit_value_add<unit_value_power<a, 2>, unit_value_power<b, 2>>>` to
* represent `c = sqrt(a^2 + b^2).
*/
/**
* @defgroup UnitMath Unit Math
* @brief Defines a collection of unit-enabled, strongly-typed versions of `<cmath>` functions.
* @details Includes most c++11 extensions.
*/
/**
* @defgroup Conversion Explicit Conversion
* @brief Functions used to convert values of one logical type to another.
*/
/**
* @defgroup TypeTraits Type Traits
* @brief Defines a series of classes to obtain unit type information at compile-time.
*/
//------------------------------
// FORWARD DECLARATIONS
//------------------------------
/** @cond */ // DOXYGEN IGNORE
namespace constants
{
namespace detail
{
static constexpr const UNIT_LIB_DEFAULT_TYPE PI_VAL = 3.14159265358979323846264338327950288419716939937510;
}
}
/** @endcond */ // END DOXYGEN IGNORE
//------------------------------
// RATIO TRAITS
//------------------------------
/**
* @ingroup TypeTraits
* @{
*/
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/// has_num implementation.
template<class T>
struct has_num_impl
{
template<class U>
static constexpr auto test(U*)->std::is_integral<decltype(U::num)> {return std::is_integral<decltype(U::num)>{}; }
template<typename>
static constexpr std::false_type test(...) { return std::false_type{}; }
using type = decltype(test<T>(0));
};
}
/**
* @brief Trait which checks for the existence of a static numerator.
* @details Inherits from `std::true_type` or `std::false_type`. Use `has_num<T>::value` to test
* whether `class T` has a numerator static member.
*/
template<class T>
struct has_num : units::detail::has_num_impl<T>::type {};
namespace detail
{
/// has_den implementation.
template<class T>
struct has_den_impl
{
template<class U>
static constexpr auto test(U*)->std::is_integral<decltype(U::den)> { return std::is_integral<decltype(U::den)>{}; }
template<typename>
static constexpr std::false_type test(...) { return std::false_type{}; }
using type = decltype(test<T>(0));
};
}
/**
* @brief Trait which checks for the existence of a static denominator.
* @details Inherits from `std::true_type` or `std::false_type`. Use `has_den<T>::value` to test
* whether `class T` has a denominator static member.
*/
template<class T>
struct has_den : units::detail::has_den_impl<T>::type {};
/** @endcond */ // END DOXYGEN IGNORE
namespace traits
{
/**
* @brief Trait that tests whether a type represents a std::ratio.
* @details Inherits from `std::true_type` or `std::false_type`. Use `is_ratio<T>::value` to test
* whether `class T` implements a std::ratio.
*/
template<class T>
struct is_ratio : std::integral_constant<bool,
has_num<T>::value &&
has_den<T>::value>
{};
}
//------------------------------
// UNIT TRAITS
//------------------------------
/** @cond */ // DOXYGEN IGNORE
/**
* @brief void type.
* @details Helper class for creating type traits.
*/
template<class ...>
struct void_t { typedef void type; };
/**
* @brief parameter pack for boolean arguments.
*/
template<bool...> struct bool_pack {};
/**
* @brief Trait which tests that a set of other traits are all true.
*/
template<bool... Args>
struct all_true : std::is_same<units::bool_pack<true, Args...>, units::bool_pack<Args..., true>> {};
/** @endcond */ // DOXYGEN IGNORE
/**
* @brief namespace representing type traits which can access the properties of types provided by the units library.
*/
namespace traits
{
#ifdef FOR_DOXYGEN_PURPOSES_ONLY
/**
* @ingroup TypeTraits
* @brief Traits class defining the properties of units.
* @details The units library determines certain properties of the units passed to
* them and what they represent by using the members of the corresponding
* unit_traits instantiation.
*/
template<class T>
struct unit_traits
{
typedef typename T::base_unit_type base_unit_type; ///< Unit type that the unit was derived from. May be a `base_unit` or another `unit`. Use the `base_unit_of` trait to find the SI base unit type. This will be `void` if type `T` is not a unit.
typedef typename T::conversion_ratio conversion_ratio; ///< `std::ratio` representing the conversion factor to the `base_unit_type`. This will be `void` if type `T` is not a unit.
typedef typename T::pi_exponent_ratio pi_exponent_ratio; ///< `std::ratio` representing the exponent of pi to be used in the conversion. This will be `void` if type `T` is not a unit.
typedef typename T::translation_ratio translation_ratio; ///< `std::ratio` representing a datum translation to the base unit (i.e. degrees C to degrees F conversion). This will be `void` if type `T` is not a unit.
};
#endif
/** @cond */ // DOXYGEN IGNORE
/**
* @brief unit traits implementation for classes which are not units.
*/
template<class T, typename = void>
struct unit_traits
{
typedef void base_unit_type;
typedef void conversion_ratio;
typedef void pi_exponent_ratio;
typedef void translation_ratio;
};
template<class T>
struct unit_traits
<T, typename void_t<
typename T::base_unit_type,
typename T::conversion_ratio,
typename T::pi_exponent_ratio,
typename T::translation_ratio>::type>
{
typedef typename T::base_unit_type base_unit_type; ///< Unit type that the unit was derived from. May be a `base_unit` or another `unit`. Use the `base_unit_of` trait to find the SI base unit type. This will be `void` if type `T` is not a unit.
typedef typename T::conversion_ratio conversion_ratio; ///< `std::ratio` representing the conversion factor to the `base_unit_type`. This will be `void` if type `T` is not a unit.
typedef typename T::pi_exponent_ratio pi_exponent_ratio; ///< `std::ratio` representing the exponent of pi to be used in the conversion. This will be `void` if type `T` is not a unit.
typedef typename T::translation_ratio translation_ratio; ///< `std::ratio` representing a datum translation to the base unit (i.e. degrees C to degrees F conversion). This will be `void` if type `T` is not a unit.
};
/** @endcond */ // END DOXYGEN IGNORE
}
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief helper type to identify base units.
* @details A non-templated base class for `base_unit` which enables RTTI testing.
*/
struct _base_unit_t {};
}
/** @endcond */ // END DOXYGEN IGNORE
namespace traits
{
/**
* @ingroup TypeTraits
* @brief Trait which tests if a class is a `base_unit` type.
* @details Inherits from `std::true_type` or `std::false_type`. Use `is_base_unit<T>::value` to test
* whether `class T` implements a `base_unit`.
*/
template<class T>
struct is_base_unit : std::is_base_of<units::detail::_base_unit_t, T> {};
}
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief helper type to identify units.
* @details A non-templated base class for `unit` which enables RTTI testing.
*/
struct _unit {};
template<std::intmax_t Num, std::intmax_t Den = 1>
using meter_ratio = std::ratio<Num, Den>;
}
/** @endcond */ // END DOXYGEN IGNORE
namespace traits
{
/**
* @ingroup TypeTraits
* @brief Traits which tests if a class is a `unit`
* @details Inherits from `std::true_type` or `std::false_type`. Use `is_unit<T>::value` to test
* whether `class T` implements a `unit`.
*/
template<class T>
struct is_unit : std::is_base_of<units::detail::_unit, T>::type {};
}
/** @} */ // end of TypeTraits
//------------------------------
// BASE UNIT CLASS
//------------------------------
/**
* @ingroup UnitTypes
* @brief Class representing SI base unit types.
* @details Base units are represented by a combination of `std::ratio` template parameters, each
* describing the exponent of the type of unit they represent. Example: meters per second
* would be described by a +1 exponent for meters, and a -1 exponent for seconds, thus:
* `base_unit<std::ratio<1>, std::ratio<0>, std::ratio<-1>>`
* @tparam Meter `std::ratio` representing the exponent value for meters.
* @tparam Kilogram `std::ratio` representing the exponent value for kilograms.
* @tparam Second `std::ratio` representing the exponent value for seconds.
* @tparam Radian `std::ratio` representing the exponent value for radians. Although radians are not SI base units, they are included because radians are described by the SI as m * m^-1, which would make them indistinguishable from scalars.
* @tparam Ampere `std::ratio` representing the exponent value for amperes.
* @tparam Kelvin `std::ratio` representing the exponent value for Kelvin.
* @tparam Mole `std::ratio` representing the exponent value for moles.
* @tparam Candela `std::ratio` representing the exponent value for candelas.
* @tparam Byte `std::ratio` representing the exponent value for bytes.
* @sa category for type aliases for SI base_unit types.
*/
template<class Meter = detail::meter_ratio<0>,
class Kilogram = std::ratio<0>,
class Second = std::ratio<0>,
class Radian = std::ratio<0>,
class Ampere = std::ratio<0>,
class Kelvin = std::ratio<0>,
class Mole = std::ratio<0>,
class Candela = std::ratio<0>,
class Byte = std::ratio<0>>
struct base_unit : units::detail::_base_unit_t
{
static_assert(traits::is_ratio<Meter>::value, "Template parameter `Meter` must be a `std::ratio` representing the exponent of meters the unit has");
static_assert(traits::is_ratio<Kilogram>::value, "Template parameter `Kilogram` must be a `std::ratio` representing the exponent of kilograms the unit has");
static_assert(traits::is_ratio<Second>::value, "Template parameter `Second` must be a `std::ratio` representing the exponent of seconds the unit has");
static_assert(traits::is_ratio<Ampere>::value, "Template parameter `Ampere` must be a `std::ratio` representing the exponent of amperes the unit has");
static_assert(traits::is_ratio<Kelvin>::value, "Template parameter `Kelvin` must be a `std::ratio` representing the exponent of kelvin the unit has");
static_assert(traits::is_ratio<Candela>::value, "Template parameter `Candela` must be a `std::ratio` representing the exponent of candelas the unit has");
static_assert(traits::is_ratio<Mole>::value, "Template parameter `Mole` must be a `std::ratio` representing the exponent of moles the unit has");
static_assert(traits::is_ratio<Radian>::value, "Template parameter `Radian` must be a `std::ratio` representing the exponent of radians the unit has");
static_assert(traits::is_ratio<Byte>::value, "Template parameter `Byte` must be a `std::ratio` representing the exponent of bytes the unit has");
typedef Meter meter_ratio;
typedef Kilogram kilogram_ratio;
typedef Second second_ratio;
typedef Radian radian_ratio;
typedef Ampere ampere_ratio;
typedef Kelvin kelvin_ratio;
typedef Mole mole_ratio;
typedef Candela candela_ratio;
typedef Byte byte_ratio;
};
//------------------------------
// UNIT CATEGORIES
//------------------------------
/**
* @brief namespace representing the implemented base and derived unit types. These will not generally be needed by library users.
* @sa base_unit for the definition of the category parameters.
*/
namespace category
{
// SCALAR (DIMENSIONLESS) TYPES
typedef base_unit<> scalar_unit; ///< Represents a quantity with no dimension.
typedef base_unit<> dimensionless_unit; ///< Represents a quantity with no dimension.
// SI BASE UNIT TYPES
// METERS KILOGRAMS SECONDS RADIANS AMPERES KELVIN MOLE CANDELA BYTE --- CATEGORY
typedef base_unit<detail::meter_ratio<1>> length_unit; ///< Represents an SI base unit of length
typedef base_unit<detail::meter_ratio<0>, std::ratio<1>> mass_unit; ///< Represents an SI base unit of mass
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<1>> time_unit; ///< Represents an SI base unit of time
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>> angle_unit; ///< Represents an SI base unit of angle
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>> current_unit; ///< Represents an SI base unit of current
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>> temperature_unit; ///< Represents an SI base unit of temperature
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>> substance_unit; ///< Represents an SI base unit of amount of substance
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>> luminous_intensity_unit; ///< Represents an SI base unit of luminous intensity
// SI DERIVED UNIT TYPES
// METERS KILOGRAMS SECONDS RADIANS AMPERES KELVIN MOLE CANDELA BYTE --- CATEGORY
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<2>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>> solid_angle_unit; ///< Represents an SI derived unit of solid angle
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<-1>> frequency_unit; ///< Represents an SI derived unit of frequency
typedef base_unit<detail::meter_ratio<1>, std::ratio<0>, std::ratio<-1>> velocity_unit; ///< Represents an SI derived unit of velocity
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<-1>, std::ratio<1>> angular_velocity_unit; ///< Represents an SI derived unit of angular velocity
typedef base_unit<detail::meter_ratio<1>, std::ratio<0>, std::ratio<-2>> acceleration_unit; ///< Represents an SI derived unit of acceleration
typedef base_unit<detail::meter_ratio<1>, std::ratio<0>, std::ratio<-3>> jerk_unit; ///< Represents an SI derived unit of jerk
typedef base_unit<detail::meter_ratio<1>, std::ratio<1>, std::ratio<-2>> force_unit; ///< Represents an SI derived unit of force
typedef base_unit<detail::meter_ratio<-1>, std::ratio<1>, std::ratio<-2>> pressure_unit; ///< Represents an SI derived unit of pressure
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<1>, std::ratio<0>, std::ratio<1>> charge_unit; ///< Represents an SI derived unit of charge
typedef base_unit<detail::meter_ratio<2>, std::ratio<1>, std::ratio<-2>> energy_unit; ///< Represents an SI derived unit of energy
typedef base_unit<detail::meter_ratio<2>, std::ratio<1>, std::ratio<-3>> power_unit; ///< Represents an SI derived unit of power
typedef base_unit<detail::meter_ratio<2>, std::ratio<1>, std::ratio<-3>, std::ratio<0>, std::ratio<-1>> voltage_unit; ///< Represents an SI derived unit of voltage
typedef base_unit<detail::meter_ratio<-2>, std::ratio<-1>, std::ratio<4>, std::ratio<0>, std::ratio<2>> capacitance_unit; ///< Represents an SI derived unit of capacitance
typedef base_unit<detail::meter_ratio<2>, std::ratio<1>, std::ratio<-3>, std::ratio<0>, std::ratio<-2>> impedance_unit; ///< Represents an SI derived unit of impedance
typedef base_unit<detail::meter_ratio<-2>, std::ratio<-1>, std::ratio<3>, std::ratio<0>, std::ratio<2>> conductance_unit; ///< Represents an SI derived unit of conductance
typedef base_unit<detail::meter_ratio<2>, std::ratio<1>, std::ratio<-2>, std::ratio<0>, std::ratio<-1>> magnetic_flux_unit; ///< Represents an SI derived unit of magnetic flux
typedef base_unit<detail::meter_ratio<0>, std::ratio<1>, std::ratio<-2>, std::ratio<0>, std::ratio<-1>> magnetic_field_strength_unit; ///< Represents an SI derived unit of magnetic field strength
typedef base_unit<detail::meter_ratio<2>, std::ratio<1>, std::ratio<-2>, std::ratio<0>, std::ratio<-2>> inductance_unit; ///< Represents an SI derived unit of inductance
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<2>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>> luminous_flux_unit; ///< Represents an SI derived unit of luminous flux
typedef base_unit<detail::meter_ratio<-2>, std::ratio<0>, std::ratio<0>, std::ratio<2>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>> illuminance_unit; ///< Represents an SI derived unit of illuminance
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<-1>> radioactivity_unit; ///< Represents an SI derived unit of radioactivity
// OTHER UNIT TYPES
// METERS KILOGRAMS SECONDS RADIANS AMPERES KELVIN MOLE CANDELA BYTE --- CATEGORY
typedef base_unit<detail::meter_ratio<2>, std::ratio<1>, std::ratio<-2>> torque_unit; ///< Represents an SI derived unit of torque
typedef base_unit<detail::meter_ratio<2>> area_unit; ///< Represents an SI derived unit of area
typedef base_unit<detail::meter_ratio<3>> volume_unit; ///< Represents an SI derived unit of volume
typedef base_unit<detail::meter_ratio<-3>, std::ratio<1>> density_unit; ///< Represents an SI derived unit of density
typedef base_unit<> concentration_unit; ///< Represents a unit of concentration
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>> data_unit; ///< Represents a unit of data size
typedef base_unit<detail::meter_ratio<0>, std::ratio<0>, std::ratio<-1>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<0>, std::ratio<1>> data_transfer_rate_unit; ///< Represents a unit of data transfer rate
}
//------------------------------
// UNIT CLASSES
//------------------------------
/** @cond */ // DOXYGEN IGNORE
/**
* @brief unit type template specialization for units derived from base units.
*/
template <class, class, class, class> struct unit;
template<class Conversion, class... Exponents, class PiExponent, class Translation>
struct unit<Conversion, base_unit<Exponents...>, PiExponent, Translation> : units::detail::_unit
{
static_assert(traits::is_ratio<Conversion>::value, "Template parameter `Conversion` must be a `std::ratio` representing the conversion factor to `BaseUnit`.");
static_assert(traits::is_ratio<PiExponent>::value, "Template parameter `PiExponent` must be a `std::ratio` representing the exponents of Pi the unit has.");
static_assert(traits::is_ratio<Translation>::value, "Template parameter `Translation` must be a `std::ratio` representing an additive translation required by the unit conversion.");
typedef typename units::base_unit<Exponents...> base_unit_type;
typedef Conversion conversion_ratio;
typedef Translation translation_ratio;
typedef PiExponent pi_exponent_ratio;
};
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief Type representing an arbitrary unit.
* @ingroup UnitTypes
* @details `unit` types are used as tags for the `conversion` function. They are *not* containers
* (see `unit_t` for a container class). Each unit is defined by:
*
* - A `std::ratio` defining the conversion factor to the base unit type. (e.g. `std::ratio<1,12>` for inches to feet)
* - A base unit that the unit is derived from (or a unit category. Must be of type `unit` or `base_unit`)
* - An exponent representing factors of PI required by the conversion. (e.g. `std::ratio<-1>` for a radians to degrees conversion)
* - a ratio representing a datum translation required for the conversion (e.g. `std::ratio<32>` for a fahrenheit to celsius conversion)
*
* Typically, a specific unit, like `meters`, would be implemented as a type alias
* of `unit`, i.e. `using meters = unit<std::ratio<1>, units::category::length_unit`, or
* `using inches = unit<std::ratio<1,12>, feet>`.
* @tparam Conversion std::ratio representing scalar multiplication factor.
* @tparam BaseUnit Unit type which this unit is derived from. May be a `base_unit`, or another `unit`.
* @tparam PiExponent std::ratio representing the exponent of pi required by the conversion.
* @tparam Translation std::ratio representing any datum translation required by the conversion.
*/
template<class Conversion, class BaseUnit, class PiExponent = std::ratio<0>, class Translation = std::ratio<0>>
struct unit : units::detail::_unit
{
static_assert(traits::is_unit<BaseUnit>::value, "Template parameter `BaseUnit` must be a `unit` type.");
static_assert(traits::is_ratio<Conversion>::value, "Template parameter `Conversion` must be a `std::ratio` representing the conversion factor to `BaseUnit`.");
static_assert(traits::is_ratio<PiExponent>::value, "Template parameter `PiExponent` must be a `std::ratio` representing the exponents of Pi the unit has.");
typedef typename units::traits::unit_traits<BaseUnit>::base_unit_type base_unit_type;
typedef typename std::ratio_multiply<typename BaseUnit::conversion_ratio, Conversion> conversion_ratio;
typedef typename std::ratio_add<typename BaseUnit::pi_exponent_ratio, PiExponent> pi_exponent_ratio;
typedef typename std::ratio_add<std::ratio_multiply<typename BaseUnit::conversion_ratio, Translation>, typename BaseUnit::translation_ratio> translation_ratio;
};
//------------------------------
// BASE UNIT MANIPULATORS
//------------------------------
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief base_unit_of trait implementation
* @details recursively seeks base_unit type that a unit is derived from. Since units can be
* derived from other units, the `base_unit_type` typedef may not represent this value.
*/
template<class> struct base_unit_of_impl;
template<class Conversion, class BaseUnit, class PiExponent, class Translation>
struct base_unit_of_impl<unit<Conversion, BaseUnit, PiExponent, Translation>> : base_unit_of_impl<BaseUnit> {};
template<class... Exponents>
struct base_unit_of_impl<base_unit<Exponents...>>
{
typedef base_unit<Exponents...> type;
};
template<>
struct base_unit_of_impl<void>
{
typedef void type;
};
}
/** @endcond */ // END DOXYGEN IGNORE
namespace traits
{
/**
* @brief Trait which returns the `base_unit` type that a unit is originally derived from.
* @details Since units can be derived from other `unit` types in addition to `base_unit` types,
* the `base_unit_type` typedef will not always be a `base_unit` (or unit category).
* Since compatible
*/
template<class U>
using base_unit_of = typename units::detail::base_unit_of_impl<U>::type;
}
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief implementation of base_unit_multiply
* @details 'multiples' (adds exponent ratios of) two base unit types. Base units can be found
* using `base_unit_of`.
*/
template<class, class> struct base_unit_multiply_impl;
template<class... Exponents1, class... Exponents2>
struct base_unit_multiply_impl<base_unit<Exponents1...>, base_unit<Exponents2...>> {
using type = base_unit<std::ratio_add<Exponents1, Exponents2>...>;
};
/**
* @brief represents type of two base units multiplied together
*/
template<class U1, class U2>
using base_unit_multiply = typename base_unit_multiply_impl<U1, U2>::type;
/**
* @brief implementation of base_unit_divide
* @details 'dived' (subtracts exponent ratios of) two base unit types. Base units can be found
* using `base_unit_of`.
*/
template<class, class> struct base_unit_divide_impl;
template<class... Exponents1, class... Exponents2>
struct base_unit_divide_impl<base_unit<Exponents1...>, base_unit<Exponents2...>> {
using type = base_unit<std::ratio_subtract<Exponents1, Exponents2>...>;
};
/**
* @brief represents the resulting type of `base_unit` U1 divided by U2.
*/
template<class U1, class U2>
using base_unit_divide = typename base_unit_divide_impl<U1, U2>::type;
/**
* @brief implementation of inverse_base
* @details multiplies all `base_unit` exponent ratios by -1. The resulting type represents
* the inverse base unit of the given `base_unit` type.
*/
template<class> struct inverse_base_impl;
template<class... Exponents>
struct inverse_base_impl<base_unit<Exponents...>> {
using type = base_unit<std::ratio_multiply<Exponents, std::ratio<-1>>...>;
};
/**
* @brief represent the inverse type of `class U`
* @details E.g. if `U` is `length_unit`, then `inverse<U>` will represent `length_unit^-1`.
*/
template<class U> using inverse_base = typename inverse_base_impl<U>::type;
/**
* @brief implementation of `squared_base`
* @details multiplies all the exponent ratios of the given class by 2. The resulting type is
* equivalent to the given type squared.
*/
template<class U> struct squared_base_impl;
template<class... Exponents>
struct squared_base_impl<base_unit<Exponents...>> {
using type = base_unit<std::ratio_multiply<Exponents, std::ratio<2>>...>;
};
/**
* @brief represents the type of a `base_unit` squared.
* @details E.g. `squared<length_unit>` will represent `length_unit^2`.
*/
template<class U> using squared_base = typename squared_base_impl<U>::type;
/**
* @brief implementation of `cubed_base`
* @details multiplies all the exponent ratios of the given class by 3. The resulting type is
* equivalent to the given type cubed.
*/
template<class U> struct cubed_base_impl;
template<class... Exponents>
struct cubed_base_impl<base_unit<Exponents...>> {
using type = base_unit<std::ratio_multiply<Exponents, std::ratio<3>>...>;
};