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FalconLibraryCPP/libs/units/units.h

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Use units in TimedTrajectory
2019-06-27 20:47:47 +00:00
//--------------------------------------------------------------------------------------------------
//
// 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(_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 <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* 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,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 abbreviation - abbreviated unit name, e.g. 'm'
*/
#define UNIT_ADD_NAME(namespaceName, nameSingular, 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;\
}
/**
* @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, 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<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 farenheit 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>>...>;
};
/**
* @brief represents the type of a `base_unit` cubed.
* @details E.g. `cubed<length_unit>` will represent `length_unit^3`.
*/
template<class U> using cubed_base = typename cubed_base_impl<U>::type;
/**
* @brief implementation of `sqrt_base`
* @details divides all the exponent ratios of the given class by 2. The resulting type is
* equivalent to the square root of the given type.
*/
template<class U> struct sqrt_base_impl;
template<class... Exponents>
struct sqrt_base_impl<base_unit<Exponents...>> {
using type = base_unit<std::ratio_divide<Exponents, std::ratio<2>>...>;
};
/**
* @brief represents the square-root type of a `base_unit`.
* @details E.g. `sqrt<length_unit>` will represent `length_unit^(1/2)`.
*/
template<class U> using sqrt_base = typename sqrt_base_impl<U>::type;
/**
* @brief implementation of `cbrt_base`
* @details divides all the exponent ratios of the given class by 3. The resulting type is
* equivalent to the given type's cube-root.
*/
template<class U> struct cbrt_base_impl;
template<class... Exponents>
struct cbrt_base_impl<base_unit<Exponents...>> {
using type = base_unit<std::ratio_divide<Exponents, std::ratio<3>>...>;
};
/**
* @brief represents the cube-root type of a `base_unit` .
* @details E.g. `cbrt<length_unit>` will represent `length_unit^(1/3)`.
*/
template<class U> using cbrt_base = typename cbrt_base_impl<U>::type;
}
/** @endcond */ // END DOXYGEN IGNORE
//------------------------------
// UNIT MANIPULATORS
//------------------------------
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief implementation of `unit_multiply`.
* @details multiplies two units. The base unit becomes the base units of each with their exponents
* added together. The conversion factors of each are multiplied by each other. Pi exponent ratios
* are added, and datum translations are removed.
*/
template<class Unit1, class Unit2>
struct unit_multiply_impl
{
using type = unit < std::ratio_multiply<typename Unit1::conversion_ratio, typename Unit2::conversion_ratio>,
base_unit_multiply <traits::base_unit_of<typename Unit1::base_unit_type>, traits::base_unit_of<typename Unit2::base_unit_type>>,
std::ratio_add<typename Unit1::pi_exponent_ratio, typename Unit2::pi_exponent_ratio>,
std::ratio < 0 >> ;
};
/**
* @brief represents the type of two units multiplied together.
* @details recalculates conversion and exponent ratios at compile-time.
*/
template<class U1, class U2>
using unit_multiply = typename unit_multiply_impl<U1, U2>::type;
/**
* @brief implementation of `unit_divide`.
* @details divides two units. The base unit becomes the base units of each with their exponents
* subtracted from each other. The conversion factors of each are divided by each other. Pi exponent ratios
* are subtracted, and datum translations are removed.
*/
template<class Unit1, class Unit2>
struct unit_divide_impl
{
using type = unit < std::ratio_divide<typename Unit1::conversion_ratio, typename Unit2::conversion_ratio>,
base_unit_divide<traits::base_unit_of<typename Unit1::base_unit_type>, traits::base_unit_of<typename Unit2::base_unit_type>>,
std::ratio_subtract<typename Unit1::pi_exponent_ratio, typename Unit2::pi_exponent_ratio>,
std::ratio < 0 >> ;
};
/**
* @brief represents the type of two units divided by each other.
* @details recalculates conversion and exponent ratios at compile-time.
*/
template<class U1, class U2>
using unit_divide = typename unit_divide_impl<U1, U2>::type;
/**
* @brief implementation of `inverse`
* @details inverts a unit (equivalent to 1/unit). The `base_unit` and pi exponents are all multiplied by
* -1. The conversion ratio numerator and denominator are swapped. Datum translation
* ratios are removed.
*/
template<class Unit>
struct inverse_impl
{
using type = unit < std::ratio<Unit::conversion_ratio::den, Unit::conversion_ratio::num>,
inverse_base<traits::base_unit_of<typename units::traits::unit_traits<Unit>::base_unit_type>>,
std::ratio_multiply<typename units::traits::unit_traits<Unit>::pi_exponent_ratio, std::ratio<-1>>,
std::ratio < 0 >> ; // inverses are rates or change, the translation factor goes away.
};
}
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief represents the inverse unit type of `class U`.
* @ingroup UnitManipulators
* @tparam U `unit` type to invert.
* @details E.g. `inverse<meters>` will represent meters^-1 (i.e. 1/meters).
*/
template<class U> using inverse = typename units::detail::inverse_impl<U>::type;
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief implementation of `squared`
* @details Squares the conversion ratio, `base_unit` exponents, pi exponents, and removes
* datum translation ratios.
*/
template<class Unit>
struct squared_impl
{
static_assert(traits::is_unit<Unit>::value, "Template parameter `Unit` must be a `unit` type.");
using Conversion = typename Unit::conversion_ratio;
using type = unit < std::ratio_multiply<Conversion, Conversion>,
squared_base<traits::base_unit_of<typename Unit::base_unit_type>>,
std::ratio_multiply<typename Unit::pi_exponent_ratio, std::ratio<2>>,
typename Unit::translation_ratio
> ;
};
}
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief represents the unit type of `class U` squared
* @ingroup UnitManipulators
* @tparam U `unit` type to square.
* @details E.g. `square<meters>` will represent meters^2.
*/
template<class U>
using squared = typename units::detail::squared_impl<U>::type;
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief implementation of `cubed`
* @details Cubes the conversion ratio, `base_unit` exponents, pi exponents, and removes
* datum translation ratios.
*/
template<class Unit>
struct cubed_impl
{
static_assert(traits::is_unit<Unit>::value, "Template parameter `Unit` must be a `unit` type.");
using Conversion = typename Unit::conversion_ratio;
using type = unit < std::ratio_multiply<Conversion, std::ratio_multiply<Conversion, Conversion>>,
cubed_base<traits::base_unit_of<typename Unit::base_unit_type>>,
std::ratio_multiply<typename Unit::pi_exponent_ratio, std::ratio<3>>,
typename Unit::translation_ratio> ;
};
}
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief represents the type of `class U` cubed.
* @ingroup UnitManipulators
* @tparam U `unit` type to cube.
* @details E.g. `cubed<meters>` will represent meters^3.
*/
template<class U>
using cubed = typename units::detail::cubed_impl<U>::type;
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
//----------------------------------
// RATIO_SQRT IMPLEMENTATION
//----------------------------------
using Zero = std::ratio<0>;
using One = std::ratio<1>;
template <typename R> using Square = std::ratio_multiply<R, R>;
// Find the largest std::integer N such that Predicate<N>::value is true.
template <template <std::intmax_t N> class Predicate, typename enabled = void>
struct BinarySearch {
template <std::intmax_t N>
struct SafeDouble_ {
static constexpr const std::intmax_t value = 2 * N;
static_assert(value > 0, "Overflows when computing 2 * N");
};
template <intmax_t Lower, intmax_t Upper, typename Condition1 = void, typename Condition2 = void>
struct DoubleSidedSearch_ : DoubleSidedSearch_<Lower, Upper,
std::integral_constant<bool, (Upper - Lower == 1)>,
std::integral_constant<bool, ((Upper - Lower>1 && Predicate<Lower + (Upper - Lower) / 2>::value))>> {};
template <intmax_t Lower, intmax_t Upper>
struct DoubleSidedSearch_<Lower, Upper, std::false_type, std::false_type> : DoubleSidedSearch_<Lower, Lower + (Upper - Lower) / 2> {};
template <intmax_t Lower, intmax_t Upper, typename Condition2>
struct DoubleSidedSearch_<Lower, Upper, std::true_type, Condition2> : std::integral_constant<intmax_t, Lower>{};
template <intmax_t Lower, intmax_t Upper, typename Condition1>
struct DoubleSidedSearch_<Lower, Upper, Condition1, std::true_type> : DoubleSidedSearch_<Lower + (Upper - Lower) / 2, Upper>{};
template <std::intmax_t Lower, class enabled1 = void>
struct SingleSidedSearch_ : SingleSidedSearch_<Lower, std::integral_constant<bool, Predicate<SafeDouble_<Lower>::value>::value>>{};
template <std::intmax_t Lower>
struct SingleSidedSearch_<Lower, std::false_type> : DoubleSidedSearch_<Lower, SafeDouble_<Lower>::value> {};
template <std::intmax_t Lower>
struct SingleSidedSearch_<Lower, std::true_type> : SingleSidedSearch_<SafeDouble_<Lower>::value>{};
static constexpr const std::intmax_t value = SingleSidedSearch_<1>::value;
};
template <template <std::intmax_t N> class Predicate>
struct BinarySearch<Predicate, std::enable_if_t<!Predicate<1>::value>> : std::integral_constant<std::intmax_t, 0>{};
// Find largest std::integer N such that N<=sqrt(R)
template <typename R>
struct Integer {
template <std::intmax_t N> using Predicate_ = std::ratio_less_equal<std::ratio<N>, std::ratio_divide<R, std::ratio<N>>>;
static constexpr const std::intmax_t value = BinarySearch<Predicate_>::value;
};
template <typename R>
struct IsPerfectSquare {
static constexpr const std::intmax_t DenSqrt_ = Integer<std::ratio<R::den>>::value;
static constexpr const std::intmax_t NumSqrt_ = Integer<std::ratio<R::num>>::value;
static constexpr const bool value =( DenSqrt_ * DenSqrt_ == R::den && NumSqrt_ * NumSqrt_ == R::num);
using Sqrt = std::ratio<NumSqrt_, DenSqrt_>;
};
// Represents sqrt(P)-Q.
template <typename Tp, typename Tq>
struct Remainder {
using P = Tp;
using Q = Tq;
};
// Represents 1/R = I + Rem where R is a Remainder.
template <typename R>
struct Reciprocal {
using P_ = typename R::P;
using Q_ = typename R::Q;
using Den_ = std::ratio_subtract<P_, Square<Q_>>;
using A_ = std::ratio_divide<Q_, Den_>;
using B_ = std::ratio_divide<P_, Square<Den_>>;
static constexpr const std::intmax_t I_ = (A_::num + Integer<std::ratio_multiply<B_, Square<std::ratio<A_::den>>>>::value) / A_::den;
using I = std::ratio<I_>;
using Rem = Remainder<B_, std::ratio_subtract<I, A_>>;
};
// Expands sqrt(R) to continued fraction:
// f(x)=C1+1/(C2+1/(C3+1/(...+1/(Cn+x)))) = (U*x+V)/(W*x+1) and sqrt(R)=f(Rem).
// The error |f(Rem)-V| = |(U-W*V)x/(W*x+1)| <= |U-W*V|*Rem <= |U-W*V|/I' where
// I' is the std::integer part of reciprocal of Rem.
template <typename Tr, std::intmax_t N>
struct ContinuedFraction {
template <typename T>
using Abs_ = std::conditional_t<std::ratio_less<T, Zero>::value, std::ratio_subtract<Zero, T>, T>;
using R = Tr;
using Last_ = ContinuedFraction<R, N - 1>;
using Reciprocal_ = Reciprocal<typename Last_::Rem>;
using Rem = typename Reciprocal_::Rem;
using I_ = typename Reciprocal_::I;
using Den_ = std::ratio_add<typename Last_::W, I_>;
using U = std::ratio_divide<typename Last_::V, Den_>;
using V = std::ratio_divide<std::ratio_add<typename Last_::U, std::ratio_multiply<typename Last_::V, I_>>, Den_>;
using W = std::ratio_divide<One, Den_>;
using Error = Abs_<std::ratio_divide<std::ratio_subtract<U, std::ratio_multiply<V, W>>, typename Reciprocal<Rem>::I>>;
};
template <typename Tr>
struct ContinuedFraction<Tr, 1> {
using R = Tr;
using U = One;
using V = std::ratio<Integer<R>::value>;
using W = Zero;
using Rem = Remainder<R, V>;
using Error = std::ratio_divide<One, typename Reciprocal<Rem>::I>;
};
template <typename R, typename Eps, std::intmax_t N = 1, typename enabled = void>
struct Sqrt_ : Sqrt_<R, Eps, N + 1> {};
template <typename R, typename Eps, std::intmax_t N>
struct Sqrt_<R, Eps, N, std::enable_if_t<std::ratio_less_equal<typename ContinuedFraction<R, N>::Error, Eps>::value>> {
using type = typename ContinuedFraction<R, N>::V;
};
template <typename R, typename Eps, typename enabled = void>
struct Sqrt {
static_assert(std::ratio_greater_equal<R, Zero>::value, "R can't be negative");
};
template <typename R, typename Eps>
struct Sqrt<R, Eps, std::enable_if_t<std::ratio_greater_equal<R, Zero>::value && IsPerfectSquare<R>::value>> {
using type = typename IsPerfectSquare<R>::Sqrt;
};
template <typename R, typename Eps>
struct Sqrt<R, Eps, std::enable_if_t<(std::ratio_greater_equal<R, Zero>::value && !IsPerfectSquare<R>::value)>> : Sqrt_<R, Eps>{};
}
/** @endcond */ // END DOXYGEN IGNORE
/**
* @ingroup TypeTraits
* @brief Calculate square root of a ratio at compile-time
* @details Calculates a rational approximation of the square root of the ratio. The error
* in the calculation is bounded by 1/epsilon (Eps). E.g. for the default value
* of 10000000000, the maximum error will be a/10000000000, or 1e-8, or said another way,
* the error will be on the order of 10^-9. Since these calculations are done at
* compile time, it is advisable to set epsilon to the highest value that does not
* cause an integer overflow in the calculation. If you can't compile `ratio_sqrt`
* due to overflow errors, reducing the value of epsilon sufficiently will correct
* the problem.\n\n
* `ratio_sqrt` is guaranteed to converge for all values of `Ratio` which do not
* overflow.
* @note This function provides a rational approximation, _NOT_ an exact value.
* @tparam Ratio ratio to take the square root of. This can represent any rational value,
* _not_ just integers or values with integer roots.
* @tparam Eps Value of epsilon, which represents the inverse of the maximum allowable
* error. This value should be chosen to be as high as possible before
* integer overflow errors occur in the compiler.
*/
template<typename Ratio, std::intmax_t Eps = 10000000000>
using ratio_sqrt = typename units::detail::Sqrt<Ratio, std::ratio<1, Eps>>::type;
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief implementation of `sqrt`
* @details square roots the conversion ratio, `base_unit` exponents, pi exponents, and removes
* datum translation ratios.
*/
template<class Unit, std::intmax_t Eps>
struct sqrt_impl
{
static_assert(traits::is_unit<Unit>::value, "Template parameter `Unit` must be a `unit` type.");
using Conversion = typename Unit::conversion_ratio;
using type = unit <ratio_sqrt<Conversion, Eps>,
sqrt_base<traits::base_unit_of<typename Unit::base_unit_type>>,
std::ratio_divide<typename Unit::pi_exponent_ratio, std::ratio<2>>,
typename Unit::translation_ratio>;
};
}
/** @endcond */ // END DOXYGEN IGNORE
/**
* @ingroup UnitManipulators
* @brief represents the square root of type `class U`.
* @details Calculates a rational approximation of the square root of the unit. The error
* in the calculation is bounded by 1/epsilon (Eps). E.g. for the default value
* of 10000000000, the maximum error will be a/10000000000, or 1e-8, or said another way,
* the error will be on the order of 10^-9. Since these calculations are done at
* compile time, it is advisable to set epsilon to the highest value that does not
* cause an integer overflow in the calculation. If you can't compile `ratio_sqrt`
* due to overflow errors, reducing the value of epsilon sufficiently will correct
* the problem.\n\n
* `ratio_sqrt` is guaranteed to converge for all values of `Ratio` which do not
* overflow.
* @tparam U `unit` type to take the square root of.
* @tparam Eps Value of epsilon, which represents the inverse of the maximum allowable
* error. This value should be chosen to be as high as possible before
* integer overflow errors occur in the compiler.
* @note USE WITH CAUTION. The is an approximate value. In general, squared<sqrt<meter>> != meter,
* i.e. the operation is not reversible, and it will result in propogated approximations.
* Use only when absolutely necessary.
*/
template<class U, std::intmax_t Eps = 10000000000>
using square_root = typename units::detail::sqrt_impl<U, Eps>::type;
//------------------------------
// COMPOUND UNITS
//------------------------------
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief implementation of compound_unit
* @details multiplies a variadic list of units together, and is inherited from the resulting
* type.
*/
template<class U, class... Us> struct compound_impl;
template<class U> struct compound_impl<U> { using type = U; };
template<class U1, class U2, class...Us>
struct compound_impl<U1, U2, Us...>
: compound_impl<unit_multiply<U1, U2>, Us...> {};
}
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief Represents a unit type made up from other units.
* @details Compound units are formed by multiplying the units of all the types provided in
* the template argument. Types provided must inherit from `unit`. A compound unit can
* be formed from any number of other units, and unit manipulators like `inverse` and
* `squared` are supported. E.g. to specify acceleration, on could create
* `using acceleration = compound_unit<length::meters, inverse<squared<seconds>>;`
* @tparam U... units which, when multiplied together, form the desired compound unit.
* @ingroup UnitTypes
*/
template<class U, class... Us>
using compound_unit = typename units::detail::compound_impl<U, Us...>::type;
//------------------------------
// PREFIXES
//------------------------------
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/**
* @brief prefix applicator.
* @details creates a unit type from a prefix and a unit
*/
template<class Ratio, class Unit>
struct prefix
{
static_assert(traits::is_ratio<Ratio>::value, "Template parameter `Ratio` must be a `std::ratio`.");
static_assert(traits::is_unit<Unit>::value, "Template parameter `Unit` must be a `unit` type.");
typedef typename units::unit<Ratio, Unit> type;
};
/// recursive exponential implementation
template <int N, class U>
struct power_of_ratio
{
typedef std::ratio_multiply<U, typename power_of_ratio<N - 1, U>::type> type;
};
/// End recursion
template <class U>
struct power_of_ratio<1, U>
{
typedef U type;
};
}
/** @endcond */ // END DOXYGEN IGNORE
/**
* @ingroup UnitManipulators
* @{
* @ingroup Decimal Prefixes
* @{
*/
template<class U> using atto = typename units::detail::prefix<std::atto, U>::type; ///< Represents the type of `class U` with the metric 'atto' prefix appended. @details E.g. atto<meters> represents meters*10^-18 @tparam U unit type to apply the prefix to.
template<class U> using femto = typename units::detail::prefix<std::femto,U>::type; ///< Represents the type of `class U` with the metric 'femto' prefix appended. @details E.g. femto<meters> represents meters*10^-15 @tparam U unit type to apply the prefix to.
template<class U> using pico = typename units::detail::prefix<std::pico, U>::type; ///< Represents the type of `class U` with the metric 'pico' prefix appended. @details E.g. pico<meters> represents meters*10^-12 @tparam U unit type to apply the prefix to.
template<class U> using nano = typename units::detail::prefix<std::nano, U>::type; ///< Represents the type of `class U` with the metric 'nano' prefix appended. @details E.g. nano<meters> represents meters*10^-9 @tparam U unit type to apply the prefix to.
template<class U> using micro = typename units::detail::prefix<std::micro,U>::type; ///< Represents the type of `class U` with the metric 'micro' prefix appended. @details E.g. micro<meters> represents meters*10^-6 @tparam U unit type to apply the prefix to.
template<class U> using milli = typename units::detail::prefix<std::milli,U>::type; ///< Represents the type of `class U` with the metric 'milli' prefix appended. @details E.g. milli<meters> represents meters*10^-3 @tparam U unit type to apply the prefix to.
template<class U> using centi = typename units::detail::prefix<std::centi,U>::type; ///< Represents the type of `class U` with the metric 'centi' prefix appended. @details E.g. centi<meters> represents meters*10^-2 @tparam U unit type to apply the prefix to.
template<class U> using deci = typename units::detail::prefix<std::deci, U>::type; ///< Represents the type of `class U` with the metric 'deci' prefix appended. @details E.g. deci<meters> represents meters*10^-1 @tparam U unit type to apply the prefix to.
template<class U> using deca = typename units::detail::prefix<std::deca, U>::type; ///< Represents the type of `class U` with the metric 'deca' prefix appended. @details E.g. deca<meters> represents meters*10^1 @tparam U unit type to apply the prefix to.
template<class U> using hecto = typename units::detail::prefix<std::hecto,U>::type; ///< Represents the type of `class U` with the metric 'hecto' prefix appended. @details E.g. hecto<meters> represents meters*10^2 @tparam U unit type to apply the prefix to.
template<class U> using kilo = typename units::detail::prefix<std::kilo, U>::type; ///< Represents the type of `class U` with the metric 'kilo' prefix appended. @details E.g. kilo<meters> represents meters*10^3 @tparam U unit type to apply the prefix to.
template<class U> using mega = typename units::detail::prefix<std::mega, U>::type; ///< Represents the type of `class U` with the metric 'mega' prefix appended. @details E.g. mega<meters> represents meters*10^6 @tparam U unit type to apply the prefix to.
template<class U> using giga = typename units::detail::prefix<std::giga, U>::type; ///< Represents the type of `class U` with the metric 'giga' prefix appended. @details E.g. giga<meters> represents meters*10^9 @tparam U unit type to apply the prefix to.
template<class U> using tera = typename units::detail::prefix<std::tera, U>::type; ///< Represents the type of `class U` with the metric 'tera' prefix appended. @details E.g. tera<meters> represents meters*10^12 @tparam U unit type to apply the prefix to.
template<class U> using peta = typename units::detail::prefix<std::peta, U>::type; ///< Represents the type of `class U` with the metric 'peta' prefix appended. @details E.g. peta<meters> represents meters*10^15 @tparam U unit type to apply the prefix to.
template<class U> using exa = typename units::detail::prefix<std::exa, U>::type; ///< Represents the type of `class U` with the metric 'exa' prefix appended. @details E.g. exa<meters> represents meters*10^18 @tparam U unit type to apply the prefix to.
/** @} @} */
/**
* @ingroup UnitManipulators
* @{
* @ingroup Binary Prefixes
* @{
*/
template<class U> using kibi = typename units::detail::prefix<std::ratio<1024>, U>::type; ///< Represents the type of `class U` with the binary 'kibi' prefix appended. @details E.g. kibi<bytes> represents bytes*2^10 @tparam U unit type to apply the prefix to.
template<class U> using mebi = typename units::detail::prefix<std::ratio<1048576>, U>::type; ///< Represents the type of `class U` with the binary 'mibi' prefix appended. @details E.g. mebi<bytes> represents bytes*2^20 @tparam U unit type to apply the prefix to.
template<class U> using gibi = typename units::detail::prefix<std::ratio<1073741824>, U>::type; ///< Represents the type of `class U` with the binary 'gibi' prefix appended. @details E.g. gibi<bytes> represents bytes*2^30 @tparam U unit type to apply the prefix to.
template<class U> using tebi = typename units::detail::prefix<std::ratio<1099511627776>, U>::type; ///< Represents the type of `class U` with the binary 'tebi' prefix appended. @details E.g. tebi<bytes> represents bytes*2^40 @tparam U unit type to apply the prefix to.
template<class U> using pebi = typename units::detail::prefix<std::ratio<1125899906842624>, U>::type; ///< Represents the type of `class U` with the binary 'pebi' prefix appended. @details E.g. pebi<bytes> represents bytes*2^50 @tparam U unit type to apply the prefix to.
template<class U> using exbi = typename units::detail::prefix<std::ratio<1152921504606846976>, U>::type; ///< Represents the type of `class U` with the binary 'exbi' prefix appended. @details E.g. exbi<bytes> represents bytes*2^60 @tparam U unit type to apply the prefix to.
/** @} @} */
//------------------------------
// CONVERSION TRAITS
//------------------------------
namespace traits
{
/**
* @ingroup TypeTraits
* @brief Trait which checks whether two units can be converted to each other
* @details Inherits from `std::true_type` or `std::false_type`. Use `is_convertible_unit<U1, U2>::value` to test
* whether `class U1` is convertible to `class U2`. Note: convertible has both the semantic meaning,
* (i.e. meters can be converted to feet), and the c++ meaning of conversion (type meters can be
* converted to type feet). Conversion is always symmetric, so if U1 is convertible to U2, then
* U2 will be convertible to U1.
* @tparam U1 Unit to convert from.
* @tparam U2 Unit to convert to.
* @sa is_convertible_unit_t
*/
template<class U1, class U2>
struct is_convertible_unit : std::is_same <traits::base_unit_of<typename units::traits::unit_traits<U1>::base_unit_type>,
base_unit_of<typename units::traits::unit_traits<U2>::base_unit_type >> {};
}
//------------------------------
// CONVERSION FUNCTION
//------------------------------
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
constexpr inline UNIT_LIB_DEFAULT_TYPE pow(UNIT_LIB_DEFAULT_TYPE x, unsigned long long y)
{
return y == 0 ? 1.0 : x * pow(x, y - 1);
}
constexpr inline UNIT_LIB_DEFAULT_TYPE abs(UNIT_LIB_DEFAULT_TYPE x)
{
return x < 0 ? -x : x;
}
/// convert dispatch for units which are both the same
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline constexpr T convert(const T& value, std::true_type, std::false_type, std::false_type) noexcept
{
return value;
}
/// convert dispatch for units which are both the same
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline constexpr T convert(const T& value, std::true_type, std::false_type, std::true_type) noexcept
{
return value;
}
/// convert dispatch for units which are both the same
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline constexpr T convert(const T& value, std::true_type, std::true_type, std::false_type) noexcept
{
return value;
}
/// convert dispatch for units which are both the same
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline constexpr T convert(const T& value, std::true_type, std::true_type, std::true_type) noexcept
{
return value;
}
/// convert dispatch for units of different types w/ no translation and no PI
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline constexpr T convert(const T& value, std::false_type, std::false_type, std::false_type) noexcept
{
return ((value * Ratio::num) / Ratio::den);
}
/// convert dispatch for units of different types w/ no translation, but has PI in numerator
// constepxr with PI in numerator
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline constexpr
std::enable_if_t<(PiRatio::num / PiRatio::den >= 1 && PiRatio::num % PiRatio::den == 0), T>
convert(const T& value, std::false_type, std::true_type, std::false_type) noexcept
{
return ((value * pow(constants::detail::PI_VAL, PiRatio::num / PiRatio::den) * Ratio::num) / Ratio::den);
}
/// convert dispatch for units of different types w/ no translation, but has PI in denominator
// constexpr with PI in denominator
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline constexpr
std::enable_if_t<(PiRatio::num / PiRatio::den <= -1 && PiRatio::num % PiRatio::den == 0), T>
convert(const T& value, std::false_type, std::true_type, std::false_type) noexcept
{
return (value * Ratio::num) / (Ratio::den * pow(constants::detail::PI_VAL, -PiRatio::num / PiRatio::den));
}
/// convert dispatch for units of different types w/ no translation, but has PI in numerator
// Not constexpr - uses std::pow
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline // sorry, this can't be constexpr!
std::enable_if_t<(PiRatio::num / PiRatio::den < 1 && PiRatio::num / PiRatio::den > -1), T>
convert(const T& value, std::false_type, std::true_type, std::false_type) noexcept
{
return ((value * std::pow(constants::detail::PI_VAL, PiRatio::num / PiRatio::den) * Ratio::num) / Ratio::den);
}
/// convert dispatch for units of different types with a translation, but no PI
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline constexpr T convert(const T& value, std::false_type, std::false_type, std::true_type) noexcept
{
return ((value * Ratio::num) / Ratio::den) + (static_cast<UNIT_LIB_DEFAULT_TYPE>(Translation::num) / Translation::den);
}
/// convert dispatch for units of different types with a translation AND PI
template<class UnitFrom, class UnitTo, class Ratio, class PiRatio, class Translation, typename T>
static inline constexpr T convert(const T& value, const std::false_type, const std::true_type, const std::true_type) noexcept
{
return ((value * std::pow(constants::detail::PI_VAL, PiRatio::num / PiRatio::den) * Ratio::num) / Ratio::den) + (static_cast<UNIT_LIB_DEFAULT_TYPE>(Translation::num) / Translation::den);
}
}
/** @endcond */ // END DOXYGEN IGNORE
/**
* @ingroup Conversion
* @brief converts a <i>value</i> from one type to another.
* @details Converts a <i>value</i> of a built-in arithmetic type to another unit. This does not change
* the type of <i>value</i>, only what it contains. E.g. @code double result = convert<length::meters, length::feet>(1.0); // result == 3.28084 @endcode
* @sa unit_t for implicit conversion of unit containers.
* @tparam UnitFrom unit tag to convert <i>value</i> from. Must be a `unit` type (i.e. is_unit<UnitFrom>::value == true),
* and must be convertible to `UnitTo` (i.e. is_convertible_unit<UnitFrom, UnitTo>::value == true).
* @tparam UnitTo unit tag to convert <i>value</i> to. Must be a `unit` type (i.e. is_unit<UnitTo>::value == true),
* and must be convertible from `UnitFrom` (i.e. is_convertible_unit<UnitFrom, UnitTo>::value == true).
* @tparam T type of <i>value</i>. It is inferred from <i>value</i>, and is expected to be a built-in arithmetic type.
* @param[in] value Arithmetic value to convert from `UnitFrom` to `UnitTo`. The value should represent
* a quantity in units of `UnitFrom`.
* @returns value, converted from units of `UnitFrom` to `UnitTo`.
*/
template<class UnitFrom, class UnitTo, typename T = UNIT_LIB_DEFAULT_TYPE>
static inline constexpr T convert(const T& value) noexcept
{
static_assert(traits::is_unit<UnitFrom>::value, "Template parameter `UnitFrom` must be a `unit` type.");
static_assert(traits::is_unit<UnitTo>::value, "Template parameter `UnitTo` must be a `unit` type.");
static_assert(traits::is_convertible_unit<UnitFrom, UnitTo>::value, "Units are not compatible.");
using Ratio = std::ratio_divide<typename UnitFrom::conversion_ratio, typename UnitTo::conversion_ratio>;
using PiRatio = std::ratio_subtract<typename UnitFrom::pi_exponent_ratio, typename UnitTo::pi_exponent_ratio>;
using Translation = std::ratio_divide<std::ratio_subtract<typename UnitFrom::translation_ratio, typename UnitTo::translation_ratio>, typename UnitTo::conversion_ratio>;
using isSame = typename std::is_same<std::decay_t<UnitFrom>, std::decay_t<UnitTo>>::type;
using piRequired = std::integral_constant<bool, !(std::is_same<std::ratio<0>, PiRatio>::value)>;
using translationRequired = std::integral_constant<bool, !(std::is_same<std::ratio<0>, Translation>::value)>;
return units::detail::convert<UnitFrom, UnitTo, Ratio, PiRatio, Translation, T>
(value, isSame{}, piRequired{}, translationRequired{});
}
//----------------------------------
// NON-LINEAR SCALE TRAITS
//----------------------------------
/** @cond */ // DOXYGEN IGNORE
namespace traits
{
namespace detail
{
/**
* @brief implementation of has_operator_parenthesis
* @details checks that operator() returns the same type as `Ret`
*/
template<class T, class Ret>
struct has_operator_parenthesis_impl
{
template<class U>
static constexpr auto test(U*) -> decltype(std::declval<U>()()) { return decltype(std::declval<U>()()){}; }
template<typename>
static constexpr std::false_type test(...) { return std::false_type{}; }
using type = typename std::is_same<Ret, decltype(test<T>(0))>::type;
};
}
/**
* @brief checks that `class T` has an `operator()` member which returns `Ret`
* @details used as part of the linear_scale concept.
*/
template<class T, class Ret>
struct has_operator_parenthesis : traits::detail::has_operator_parenthesis_impl<T, Ret>::type {};
}
namespace traits
{
namespace detail
{
/**
* @brief implementation of has_value_member
* @details checks for a member named `m_member` with type `Ret`
*/
template<class T, class Ret>
struct has_value_member_impl
{
template<class U>
static constexpr auto test(U* p) -> decltype(p->m_value) { return p->m_value; }
template<typename>
static constexpr auto test(...)->std::false_type { return std::false_type{}; }
using type = typename std::is_same<std::decay_t<Ret>, std::decay_t<decltype(test<T>(0))>>::type;
};
}
/**
* @brief checks for a member named `m_member` with type `Ret`
* @details used as part of the linear_scale concept checker.
*/
template<class T, class Ret>
struct has_value_member : traits::detail::has_value_member_impl<T, Ret>::type {};
}
/** @endcond */ // END DOXYGEN IGNORE
namespace traits
{
/**
* @ingroup TypeTraits
* @brief Trait which tests that `class T` meets the requirements for a non-linear scale
* @details A non-linear scale must:
* - be default constructible
* - have an `operator()` member which returns the non-linear value stored in the scale
* - have an accessible `m_value` member type which stores the linearized value in the scale.
*
* Linear/nonlinear scales are used by `units::unit` to store values and scale them
* if they represent things like dB.
*/
template<class T, class Ret>
struct is_nonlinear_scale : std::integral_constant<bool,
std::is_default_constructible<T>::value &&
has_operator_parenthesis<T, Ret>::value &&
has_value_member<T, Ret>::value &&
std::is_trivial<T>::value>
{};
}
//------------------------------
// UNIT_T TYPE TRAITS
//------------------------------
namespace traits
{
#ifdef FOR_DOXYGEN_PURPOSOES_ONLY
/**
* @ingroup TypeTraits
* @brief Trait for accessing the publically defined types of `units::unit_t`
* @details The units library determines certain properties of the unit_t types passed to them
* and what they represent by using the members of the corresponding unit_t_traits instantiation.
*/
template<typename T>
struct unit_t_traits
{
typedef typename T::non_linear_scale_type non_linear_scale_type; ///< Type of the unit_t non_linear_scale (e.g. linear_scale, decibel_scale). This property is used to enable the proper linear or logarithmic arithmetic functions.
typedef typename T::underlying_type underlying_type; ///< Underlying storage type of the `unit_t`, e.g. `double`.
typedef typename T::value_type value_type; ///< Synonym for underlying type. May be removed in future versions. Prefer underlying_type.
typedef typename T::unit_type unit_type; ///< Type of unit the `unit_t` represents, e.g. `meters`
};
#endif
/** @cond */ // DOXYGEN IGNORE
/**
* @brief unit_t_traits specialization for things which are not unit_t
* @details
*/
template<typename T, typename = void>
struct unit_t_traits
{
typedef void non_linear_scale_type;
typedef void underlying_type;
typedef void value_type;
typedef void unit_type;
};
/**
* @ingroup TypeTraits
* @brief Trait for accessing the publically defined types of `units::unit_t`
* @details
*/
template<typename T>
struct unit_t_traits <T, typename void_t<
typename T::non_linear_scale_type,
typename T::underlying_type,
typename T::value_type,
typename T::unit_type>::type>
{
typedef typename T::non_linear_scale_type non_linear_scale_type;
typedef typename T::underlying_type underlying_type;
typedef typename T::value_type value_type;
typedef typename T::unit_type unit_type;
};
/** @endcond */ // END DOXYGEN IGNORE
}
namespace traits
{
/**
* @ingroup TypeTraits
* @brief Trait which tests whether two container types derived from `unit_t` are convertible to each other
* @details Inherits from `std::true_type` or `std::false_type`. Use `is_convertible_unit_t<U1, U2>::value` to test
* whether `class U1` is convertible to `class U2`. Note: convertible has both the semantic meaning,
* (i.e. meters can be converted to feet), and the c++ meaning of conversion (type meters can be
* converted to type feet). Conversion is always symmetric, so if U1 is convertible to U2, then
* U2 will be convertible to U1.
* @tparam U1 Unit to convert from.
* @tparam U2 Unit to convert to.
* @sa is_convertible_unit
*/
template<class U1, class U2>
struct is_convertible_unit_t : std::integral_constant<bool,
is_convertible_unit<typename units::traits::unit_t_traits<U1>::unit_type, typename units::traits::unit_t_traits<U2>::unit_type>::value>
{};
}
//----------------------------------
// UNIT TYPE
//----------------------------------
/** @cond */ // DOXYGEN IGNORE
// forward declaration
template<typename T> struct linear_scale;
template<typename T> struct decibel_scale;
namespace detail
{
/**
* @brief helper type to identify units.
* @details A non-templated base class for `unit` which enables RTTI testing.
*/
struct _unit_t {};
}
/** @endcond */ // END DOXYGEN IGNORE
namespace traits
{
// forward declaration
#if !defined(_MSC_VER) || _MSC_VER > 1800 // bug in VS2013 prevents this from working
template<typename... T> struct is_dimensionless_unit;
#else
template<typename T1, typename T2 = T1, typename T3 = T1> struct is_dimensionless_unit;
#endif
/**
* @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_t : std::is_base_of<units::detail::_unit_t, T>::type {};
}
/**
* @ingroup UnitContainers
* @brief Container for values which represent quantities of a given unit.
* @details Stores a value which represents a quantity in the given units. Unit containers
* (except scalar values) are *not* convertible to built-in c++ types, in order to
* provide type safety in dimensional analysis. Unit containers *are* implicitly
* convertible to other compatible unit container types. Unit containers support
* various types of arithmetic operations, depending on their scale type.
*
* The value of a `unit_t` can only be changed on construction, or by assignment
* from another `unit_t` type. If necessary, the underlying value can be accessed
* using `operator()`: @code
* meter_t m(5.0);
* double val = m(); // val == 5.0 @endcode.
* @tparam Units unit tag for which type of units the `unit_t` represents (e.g. meters)
* @tparam T underlying type of the storage. Defaults to double.
* @tparam NonLinearScale optional scale class for the units. Defaults to linear (i.e. does
* not scale the unit value). Examples of non-linear scales could be logarithmic,
* decibel, or richter scales. Non-linear scales must adhere to the non-linear-scale
* concept, i.e. `is_nonlinear_scale<...>::value` must be `true`.
* @sa
* - \ref lengthContainers "length unit containers"
* - \ref massContainers "mass unit containers"
* - \ref timeContainers "time unit containers"
* - \ref angleContainers "angle unit containers"
* - \ref currentContainers "current unit containers"
* - \ref temperatureContainers "temperature unit containers"
* - \ref substanceContainers "substance unit containers"
* - \ref luminousIntensityContainers "luminous intensity unit containers"
* - \ref solidAngleContainers "solid angle unit containers"
* - \ref frequencyContainers "frequency unit containers"
* - \ref velocityContainers "velocity unit containers"
* - \ref angularVelocityContainers "angular velocity unit containers"
* - \ref accelerationContainers "acceleration unit containers"
* - \ref forceContainers "force unit containers"
* - \ref pressureContainers "pressure unit containers"
* - \ref chargeContainers "charge unit containers"
* - \ref energyContainers "energy unit containers"
* - \ref powerContainers "power unit containers"
* - \ref voltageContainers "voltage unit containers"
* - \ref capacitanceContainers "capacitance unit containers"
* - \ref impedanceContainers "impedance unit containers"
* - \ref magneticFluxContainers "magnetic flux unit containers"
* - \ref magneticFieldStrengthContainers "magnetic field strength unit containers"
* - \ref inductanceContainers "inductance unit containers"
* - \ref luminousFluxContainers "luminous flux unit containers"
* - \ref illuminanceContainers "illuminance unit containers"
* - \ref radiationContainers "radiation unit containers"
* - \ref torqueContainers "torque unit containers"
* - \ref areaContainers "area unit containers"
* - \ref volumeContainers "volume unit containers"
* - \ref densityContainers "density unit containers"
* - \ref concentrationContainers "concentration unit containers"
* - \ref constantContainers "constant unit containers"
*/
template<class Units, typename T = UNIT_LIB_DEFAULT_TYPE, template<typename> class NonLinearScale = linear_scale>
class unit_t : public NonLinearScale<T>, units::detail::_unit_t
{
static_assert(traits::is_unit<Units>::value, "Template parameter `Units` must be a unit tag. Check that you aren't using a unit type (_t).");
static_assert(traits::is_nonlinear_scale<NonLinearScale<T>, T>::value, "Template parameter `NonLinearScale` does not conform to the `is_nonlinear_scale` concept.");
protected:
using nls = NonLinearScale<T>;
using nls::m_value;
public:
typedef NonLinearScale<T> non_linear_scale_type; ///< Type of the non-linear scale of the unit_t (e.g. linear_scale)
typedef T underlying_type; ///< Type of the underlying storage of the unit_t (e.g. double)
typedef T value_type; ///< Synonym for underlying type. May be removed in future versions. Prefer underlying_type.
typedef Units unit_type; ///< Type of `unit` the `unit_t` represents (e.g. meters)
/**
* @ingroup Constructors
* @brief default constructor.
*/
constexpr unit_t() = default;
/**
* @brief constructor
* @details constructs a new unit_t using the non-linear scale's constructor.
* @param[in] value unit value magnitude.
* @param[in] args additional constructor arguments are forwarded to the non-linear scale constructor. Which
* args are required depends on which scale is used. For the default (linear) scale,
* no additional args are necessary.
*/
template<class... Args>
inline explicit constexpr unit_t(const T value, const Args&... args) noexcept : nls(value, args...)
{
}
/**
* @brief constructor
* @details enable implicit conversions from T types ONLY for linear scalar units
* @param[in] value value of the unit_t
*/
template<class Ty, class = typename std::enable_if<traits::is_dimensionless_unit<Units>::value && std::is_arithmetic<Ty>::value>::type>
inline constexpr unit_t(const Ty value) noexcept : nls(value)
{
}
/**
* @brief chrono constructor
* @details enable implicit conversions from std::chrono::duration types ONLY for time units
* @param[in] value value of the unit_t
*/
template<class Rep, class Period, class = std::enable_if_t<std::is_arithmetic<Rep>::value && traits::is_ratio<Period>::value>>
inline constexpr unit_t(const std::chrono::duration<Rep, Period>& value) noexcept :
nls(units::convert<unit<std::ratio<1,1000000000>, category::time_unit>, Units>(static_cast<T>(std::chrono::duration_cast<std::chrono::nanoseconds>(value).count())))
{
}
/**
* @brief copy constructor (converting)
* @details performs implicit unit conversions if required.
* @param[in] rhs unit to copy.
*/
template<class UnitsRhs, typename Ty, template<typename> class NlsRhs>
inline constexpr unit_t(const unit_t<UnitsRhs, Ty, NlsRhs>& rhs) noexcept :
nls(units::convert<UnitsRhs, Units, T>(rhs.m_value), std::true_type() /*store linear value*/)
{
}
/**
* @brief assignment
* @details performs implicit unit conversions if required
* @param[in] rhs unit to copy.
*/
template<class UnitsRhs, typename Ty, template<typename> class NlsRhs>
inline unit_t& operator=(const unit_t<UnitsRhs, Ty, NlsRhs>& rhs) noexcept
{
nls::m_value = units::convert<UnitsRhs, Units, T>(rhs.m_value);
return *this;
}
/**
* @brief assignment
* @details performs implicit conversions from built-in types ONLY for scalar units
* @param[in] rhs value to copy.
*/
template<class Ty, class = std::enable_if_t<traits::is_dimensionless_unit<Units>::value && std::is_arithmetic<Ty>::value>>
inline unit_t& operator=(const Ty& rhs) noexcept
{
nls::m_value = rhs;
return *this;
}
/**
* @brief less-than
* @details compares the linearized value of two units. Performs unit conversions if necessary.
* @param[in] rhs right-hand side unit for the comparison
* @returns true IFF the value of `this` is less than the value of `rhs`
*/
template<class UnitsRhs, typename Ty, template<typename> class NlsRhs>
inline constexpr bool operator<(const unit_t<UnitsRhs, Ty, NlsRhs>& rhs) const noexcept
{
return (nls::m_value < units::convert<UnitsRhs, Units>(rhs.m_value));
}
/**
* @brief less-than or equal
* @details compares the linearized value of two units. Performs unit conversions if necessary.
* @param[in] rhs right-hand side unit for the comparison
* @returns true IFF the value of `this` is less than or equal to the value of `rhs`
*/
template<class UnitsRhs, typename Ty, template<typename> class NlsRhs>
inline constexpr bool operator<=(const unit_t<UnitsRhs, Ty, NlsRhs>& rhs) const noexcept
{
return (nls::m_value <= units::convert<UnitsRhs, Units>(rhs.m_value));
}
/**
* @brief greater-than
* @details compares the linearized value of two units. Performs unit conversions if necessary.
* @param[in] rhs right-hand side unit for the comparison
* @returns true IFF the value of `this` is greater than the value of `rhs`
*/
template<class UnitsRhs, typename Ty, template<typename> class NlsRhs>
inline constexpr bool operator>(const unit_t<UnitsRhs, Ty, NlsRhs>& rhs) const noexcept
{
return (nls::m_value > units::convert<UnitsRhs, Units>(rhs.m_value));
}
/**
* @brief greater-than or equal
* @details compares the linearized value of two units. Performs unit conversions if necessary.
* @param[in] rhs right-hand side unit for the comparison
* @returns true IFF the value of `this` is greater than or equal to the value of `rhs`
*/
template<class UnitsRhs, typename Ty, template<typename> class NlsRhs>
inline constexpr bool operator>=(const unit_t<UnitsRhs, Ty, NlsRhs>& rhs) const noexcept
{
return (nls::m_value >= units::convert<UnitsRhs, Units>(rhs.m_value));
}
/**
* @brief equality
* @details compares the linearized value of two units. Performs unit conversions if necessary.
* @param[in] rhs right-hand side unit for the comparison
* @returns true IFF the value of `this` exactly equal to the value of rhs.
* @note This may not be suitable for all applications when the underlying_type of unit_t is a double.
*/
template<class UnitsRhs, typename Ty, template<typename> class NlsRhs, std::enable_if_t<std::is_floating_point<T>::value || std::is_floating_point<Ty>::value, int> = 0>
inline constexpr bool operator==(const unit_t<UnitsRhs, Ty, NlsRhs>& rhs) const noexcept
{
return detail::abs(nls::m_value - units::convert<UnitsRhs, Units>(rhs.m_value)) < std::numeric_limits<T>::epsilon() *
detail::abs(nls::m_value + units::convert<UnitsRhs, Units>(rhs.m_value)) ||
detail::abs(nls::m_value - units::convert<UnitsRhs, Units>(rhs.m_value)) < std::numeric_limits<T>::min();
}
template<class UnitsRhs, typename Ty, template<typename> class NlsRhs, std::enable_if_t<std::is_integral<T>::value && std::is_integral<Ty>::value, int> = 0>
inline constexpr bool operator==(const unit_t<UnitsRhs, Ty, NlsRhs>& rhs) const noexcept
{
return nls::m_value == units::convert<UnitsRhs, Units>(rhs.m_value);
}
/**
* @brief inequality
* @details compares the linearized value of two units. Performs unit conversions if necessary.
* @param[in] rhs right-hand side unit for the comparison
* @returns true IFF the value of `this` is not equal to the value of rhs.
* @note This may not be suitable for all applications when the underlying_type of unit_t is a double.
*/
template<class UnitsRhs, typename Ty, template<typename> class NlsRhs>
inline constexpr bool operator!=(const unit_t<UnitsRhs, Ty, NlsRhs>& rhs) const noexcept
{
return !(*this == rhs);
}
/**
* @brief unit value
* @returns value of the unit in it's underlying, non-safe type.
*/
inline constexpr underlying_type value() const noexcept
{
return static_cast<underlying_type>(*this);
}
/**
* @brief unit value
* @returns value of the unit converted to an arithmetic, non-safe type.
*/
template<typename Ty, class = std::enable_if_t<std::is_arithmetic<Ty>::value>>
inline constexpr Ty to() const noexcept
{
return static_cast<Ty>(*this);
}
/**
* @brief linearized unit value
* @returns linearized value of unit which has a non-linear scale. For `unit_t` types with
* linear scales, this is equivalent to `value`.
*/
template<typename Ty, class = std::enable_if_t<std::is_arithmetic<Ty>::value>>
inline constexpr Ty toLinearized() const noexcept
{
return static_cast<Ty>(m_value);
}
/**
* @brief conversion
* @details Converts to a different unit container. Units can be converted to other containers
* implicitly, but this can be used in cases where explicit notation of a conversion
* is beneficial, or where an r-value container is needed.
* @tparam U unit (not unit_t) to convert to
* @returns a unit container with the specified units containing the equivalent value to
* *this.
*/
template<class U>
inline constexpr unit_t<U> convert() const noexcept
{
static_assert(traits::is_unit<U>::value, "Template parameter `U` must be a unit type.");
return unit_t<U>(*this);
}
/**
* @brief implicit type conversion.
* @details only enabled for scalar unit types.
*/
template<class Ty, std::enable_if_t<traits::is_dimensionless_unit<Units>::value && std::is_arithmetic<Ty>::value, int> = 0>
inline constexpr operator Ty() const noexcept
{
// this conversion also resolves any PI exponents, by converting from a non-zero PI ratio to a zero-pi ratio.
return static_cast<Ty>(units::convert<Units, unit<std::ratio<1>, units::category::scalar_unit>>((*this)()));
}
/**
* @brief explicit type conversion.
* @details only enabled for non-dimensionless unit types.
*/
template<class Ty, std::enable_if_t<!traits::is_dimensionless_unit<Units>::value && std::is_arithmetic<Ty>::value, int> = 0>
inline constexpr explicit operator Ty() const noexcept
{
return static_cast<Ty>((*this)());
}
/**
* @brief chrono implicit type conversion.
* @details only enabled for time unit types.
*/
template<typename U = Units, std::enable_if_t<units::traits::is_convertible_unit<U, unit<std::ratio<1>, category::time_unit>>::value, int> = 0>
inline constexpr operator std::chrono::nanoseconds() const noexcept
{
return std::chrono::duration_cast<std::chrono::nanoseconds>(std::chrono::duration<double, std::nano>(units::convert<Units, unit<std::ratio<1,1000000000>, category::time_unit>>((*this)())));
}
/**
* @brief returns the unit name
*/
inline constexpr const char* name() const noexcept
{
return units::name(*this);
}
/**
* @brief returns the unit abbreviation
*/
inline constexpr const char* abbreviation() const noexcept
{
return units::abbreviation(*this);
}
public:
template<class U, typename Ty, template<typename> class Nlt>
friend class unit_t;
};
//------------------------------
// UNIT_T NON-MEMBER FUNCTIONS
//------------------------------
/**
* @ingroup UnitContainers
* @brief Constructs a unit container from an arithmetic type.
* @details make_unit can be used to construct a unit container from an arithmetic type, as an alternative to
* using the explicit constructor. Unlike the explicit constructor it forces the user to explicitly
* specify the units.
* @tparam UnitType Type to construct.
* @tparam Ty Arithmetic type.
* @param[in] value Arithmetic value that represents a quantity in units of `UnitType`.
*/
template<class UnitType, typename T, class = std::enable_if_t<std::is_arithmetic<T>::value>>
inline constexpr UnitType make_unit(const T value) noexcept
{
static_assert(traits::is_unit_t<UnitType>::value, "Template parameter `UnitType` must be a unit type (_t).");
return UnitType(value);
}
#if !defined(UNIT_LIB_DISABLE_IOSTREAM)
template<class Units, typename T, template<typename> class NonLinearScale>
inline std::ostream& operator<<(std::ostream& os, const unit_t<Units, T, NonLinearScale>& obj) noexcept
{
using BaseUnits = unit<std::ratio<1>, typename traits::unit_traits<Units>::base_unit_type>;
os << convert<Units, BaseUnits>(obj());
if (traits::unit_traits<Units>::base_unit_type::meter_ratio::num != 0) { os << " m"; }
if (traits::unit_traits<Units>::base_unit_type::meter_ratio::num != 0 &&
traits::unit_traits<Units>::base_unit_type::meter_ratio::num != 1) { os << "^" << traits::unit_traits<Units>::base_unit_type::meter_ratio::num; }
if (traits::unit_traits<Units>::base_unit_type::meter_ratio::den != 1) { os << "/" << traits::unit_traits<Units>::base_unit_type::meter_ratio::den; }
if (traits::unit_traits<Units>::base_unit_type::kilogram_ratio::num != 0) { os << " kg"; }
if (traits::unit_traits<Units>::base_unit_type::kilogram_ratio::num != 0 &&
traits::unit_traits<Units>::base_unit_type::kilogram_ratio::num != 1) { os << "^" << traits::unit_traits<Units>::base_unit_type::kilogram_ratio::num; }
if (traits::unit_traits<Units>::base_unit_type::kilogram_ratio::den != 1) { os << "/" << traits::unit_traits<Units>::base_unit_type::kilogram_ratio::den; }
if (traits::unit_traits<Units>::base_unit_type::second_ratio::num != 0) { os << " s"; }
if (traits::unit_traits<Units>::base_unit_type::second_ratio::num != 0 &&
traits::unit_traits<Units>::base_unit_type::second_ratio::num != 1) { os << "^" << traits::unit_traits<Units>::base_unit_type::second_ratio::num; }
if (traits::unit_traits<Units>::base_unit_type::second_ratio::den != 1) { os << "/" << traits::unit_traits<Units>::base_unit_type::second_ratio::den; }
if (traits::unit_traits<Units>::base_unit_type::ampere_ratio::num != 0) { os << " A"; }
if (traits::unit_traits<Units>::base_unit_type::ampere_ratio::num != 0 &&
traits::unit_traits<Units>::base_unit_type::ampere_ratio::num != 1) { os << "^" << traits::unit_traits<Units>::base_unit_type::ampere_ratio::num; }
if (traits::unit_traits<Units>::base_unit_type::ampere_ratio::den != 1) { os << "/" << traits::unit_traits<Units>::base_unit_type::ampere_ratio::den; }
if (traits::unit_traits<Units>::base_unit_type::kelvin_ratio::num != 0) { os << " K"; }
if (traits::unit_traits<Units>::base_unit_type::kelvin_ratio::num != 0 &&
traits::unit_traits<Units>::base_unit_type::kelvin_ratio::num != 1) { os << "^" << traits::unit_traits<Units>::base_unit_type::kelvin_ratio::num; }
if (traits::unit_traits<Units>::base_unit_type::kelvin_ratio::den != 1) { os << "/" << traits::unit_traits<Units>::base_unit_type::kelvin_ratio::den; }
if (traits::unit_traits<Units>::base_unit_type::mole_ratio::num != 0) { os << " mol"; }
if (traits::unit_traits<Units>::base_unit_type::mole_ratio::num != 0 &&
traits::unit_traits<Units>::base_unit_type::mole_ratio::num != 1) { os << "^" << traits::unit_traits<Units>::base_unit_type::mole_ratio::num; }
if (traits::unit_traits<Units>::base_unit_type::mole_ratio::den != 1) { os << "/" << traits::unit_traits<Units>::base_unit_type::mole_ratio::den; }
if (traits::unit_traits<Units>::base_unit_type::candela_ratio::num != 0) { os << " cd"; }
if (traits::unit_traits<Units>::base_unit_type::candela_ratio::num != 0 &&
traits::unit_traits<Units>::base_unit_type::candela_ratio::num != 1) { os << "^" << traits::unit_traits<Units>::base_unit_type::candela_ratio::num; }
if (traits::unit_traits<Units>::base_unit_type::candela_ratio::den != 1) { os << "/" << traits::unit_traits<Units>::base_unit_type::candela_ratio::den; }
if (traits::unit_traits<Units>::base_unit_type::radian_ratio::num != 0) { os << " rad"; }
if (traits::unit_traits<Units>::base_unit_type::radian_ratio::num != 0 &&
traits::unit_traits<Units>::base_unit_type::radian_ratio::num != 1) { os << "^" << traits::unit_traits<Units>::base_unit_type::radian_ratio::num; }
if (traits::unit_traits<Units>::base_unit_type::radian_ratio::den != 1) { os << "/" << traits::unit_traits<Units>::base_unit_type::radian_ratio::den; }
if (traits::unit_traits<Units>::base_unit_type::byte_ratio::num != 0) { os << " b"; }
if (traits::unit_traits<Units>::base_unit_type::byte_ratio::num != 0 &&
traits::unit_traits<Units>::base_unit_type::byte_ratio::num != 1) { os << "^" << traits::unit_traits<Units>::base_unit_type::byte_ratio::num; }
if (traits::unit_traits<Units>::base_unit_type::byte_ratio::den != 1) { os << "/" << traits::unit_traits<Units>::base_unit_type::byte_ratio::den; }
return os;
}
#endif
template<class Units, typename T, template<typename> class NonLinearScale, typename RhsType>
inline unit_t<Units, T, NonLinearScale>& operator+=(unit_t<Units, T, NonLinearScale>& lhs, const RhsType& rhs) noexcept
{
static_assert(traits::is_convertible_unit_t<unit_t<Units, T, NonLinearScale>, RhsType>::value ||
(traits::is_dimensionless_unit<decltype(lhs)>::value && std::is_arithmetic<RhsType>::value),
"parameters are not compatible units.");
lhs = lhs + rhs;
return lhs;
}
template<class Units, typename T, template<typename> class NonLinearScale, typename RhsType>
inline unit_t<Units, T, NonLinearScale>& operator-=(unit_t<Units, T, NonLinearScale>& lhs, const RhsType& rhs) noexcept
{
static_assert(traits::is_convertible_unit_t<unit_t<Units, T, NonLinearScale>, RhsType>::value ||
(traits::is_dimensionless_unit<decltype(lhs)>::value && std::is_arithmetic<RhsType>::value),
"parameters are not compatible units.");
lhs = lhs - rhs;
return lhs;
}
template<class Units, typename T, template<typename> class NonLinearScale, typename RhsType>
inline unit_t<Units, T, NonLinearScale>& operator*=(unit_t<Units, T, NonLinearScale>& lhs, const RhsType& rhs) noexcept
{
static_assert((traits::is_dimensionless_unit<RhsType>::value || std::is_arithmetic<RhsType>::value),
"right-hand side parameter must be dimensionless.");
lhs = lhs * rhs;
return lhs;
}
template<class Units, typename T, template<typename> class NonLinearScale, typename RhsType>
inline unit_t<Units, T, NonLinearScale>& operator/=(unit_t<Units, T, NonLinearScale>& lhs, const RhsType& rhs) noexcept
{
static_assert((traits::is_dimensionless_unit<RhsType>::value || std::is_arithmetic<RhsType>::value),
"right-hand side parameter must be dimensionless.");
lhs = lhs / rhs;
return lhs;
}
//------------------------------
// UNIT_T UNARY OPERATORS
//------------------------------
// unary addition: +T
template<class Units, typename T, template<typename> class NonLinearScale>
inline unit_t<Units, T, NonLinearScale> operator+(const unit_t<Units, T, NonLinearScale>& u) noexcept
{
return u;
}
// prefix increment: ++T
template<class Units, typename T, template<typename> class NonLinearScale>
inline unit_t<Units, T, NonLinearScale>& operator++(unit_t<Units, T, NonLinearScale>& u) noexcept
{
u = unit_t<Units, T, NonLinearScale>(u() + 1);
return u;
}
// postfix increment: T++
template<class Units, typename T, template<typename> class NonLinearScale>
inline unit_t<Units, T, NonLinearScale> operator++(unit_t<Units, T, NonLinearScale>& u, int) noexcept
{
auto ret = u;
u = unit_t<Units, T, NonLinearScale>(u() + 1);
return ret;
}
// unary addition: -T
template<class Units, typename T, template<typename> class NonLinearScale>
inline unit_t<Units, T, NonLinearScale> operator-(const unit_t<Units, T, NonLinearScale>& u) noexcept
{
return unit_t<Units, T, NonLinearScale>(-u());
}
// prefix increment: --T
template<class Units, typename T, template<typename> class NonLinearScale>
inline unit_t<Units, T, NonLinearScale>& operator--(unit_t<Units, T, NonLinearScale>& u) noexcept
{
u = unit_t<Units, T, NonLinearScale>(u() - 1);
return u;
}
// postfix increment: T--
template<class Units, typename T, template<typename> class NonLinearScale>
inline unit_t<Units, T, NonLinearScale> operator--(unit_t<Units, T, NonLinearScale>& u, int) noexcept
{
auto ret = u;
u = unit_t<Units, T, NonLinearScale>(u() - 1);
return ret;
}
//------------------------------
// UNIT_CAST
//------------------------------
/**
* @ingroup Conversion
* @brief Casts a unit container to an arithmetic type.
* @details unit_cast can be used to remove the strong typing from a unit class, and convert it
* to a built-in arithmetic type. This may be useful for compatibility with libraries
* and legacy code that don't support `unit_t` types. E.g
* @code meter_t unitVal(5);
* double value = units::unit_cast<double>(unitVal); // value = 5.0
* @endcode
* @tparam T Type to cast the unit type to. Must be a built-in arithmetic type.
* @param value Unit value to cast.
* @sa unit_t::to
*/
template<typename T, typename Units, class = std::enable_if_t<std::is_arithmetic<T>::value && traits::is_unit_t<Units>::value>>
inline constexpr T unit_cast(const Units& value) noexcept
{
return static_cast<T>(value);
}
//------------------------------
// NON-LINEAR SCALE TRAITS
//------------------------------
// forward declaration
template<typename T> struct decibel_scale;
namespace traits
{
/**
* @ingroup TypeTraits
* @brief Trait which tests whether a type is inherited from a linear scale.
* @details Inherits from `std::true_type` or `std::false_type`. Use `has_linear_scale<U1 [, U2, ...]>::value` to test
* one or more types to see if they represent unit_t's whose scale is linear.
* @tparam T one or more types to test.
*/
#if !defined(_MSC_VER) || _MSC_VER > 1800 // bug in VS2013 prevents this from working
template<typename... T>
struct has_linear_scale : std::integral_constant<bool, units::all_true<std::is_base_of<units::linear_scale<typename units::traits::unit_t_traits<T>::underlying_type>, T>::value...>::value > {};
#else
template<typename T1, typename T2 = T1, typename T3 = T1>
struct has_linear_scale : std::integral_constant<bool,
std::is_base_of<units::linear_scale<typename units::traits::unit_t_traits<T1>::underlying_type>, T1>::value &&
std::is_base_of<units::linear_scale<typename units::traits::unit_t_traits<T2>::underlying_type>, T2>::value &&
std::is_base_of<units::linear_scale<typename units::traits::unit_t_traits<T3>::underlying_type>, T3>::value> {};
#endif
/**
* @ingroup TypeTraits
* @brief Trait which tests whether a type is inherited from a decibel scale.
* @details Inherits from `std::true_type` or `std::false_type`. Use `has_decibel_scale<U1 [, U2, ...]>::value` to test
* one or more types to see if they represent unit_t's whose scale is in decibels.
* @tparam T one or more types to test.
*/
#if !defined(_MSC_VER) || _MSC_VER > 1800 // bug in VS2013 prevents this from working
template<typename... T>
struct has_decibel_scale : std::integral_constant<bool, units::all_true<std::is_base_of<units::decibel_scale<typename units::traits::unit_t_traits<T>::underlying_type>, T>::value...>::value> {};
#else
template<typename T1, typename T2 = T1, typename T3 = T1>
struct has_decibel_scale : std::integral_constant<bool,
std::is_base_of<units::decibel_scale<typename units::traits::unit_t_traits<T1>::underlying_type>, T1>::value &&
std::is_base_of<units::decibel_scale<typename units::traits::unit_t_traits<T2>::underlying_type>, T2>::value &&
std::is_base_of<units::decibel_scale<typename units::traits::unit_t_traits<T2>::underlying_type>, T3>::value> {};
#endif
/**
* @ingroup TypeTraits
* @brief Trait which tests whether two types has the same non-linear scale.
* @details Inherits from `std::true_type` or `std::false_type`. Use `is_same_scale<U1 , U2>::value` to test
* whether two types have the same non-linear scale.
* @tparam T1 left hand type.
* @tparam T2 right hand type
*/
template<typename T1, typename T2>
struct is_same_scale : std::integral_constant<bool,
std::is_same<typename units::traits::unit_t_traits<T1>::non_linear_scale_type, typename units::traits::unit_t_traits<T2>::non_linear_scale_type>::value>
{};
}
//----------------------------------
// NON-LINEAR SCALES
//----------------------------------
// Non-linear transforms are used to pre and post scale units which are defined in terms of non-
// linear functions of their current value. A good example of a non-linear scale would be a
// logarithmic or decibel scale
//------------------------------
// LINEAR SCALE
//------------------------------
/**
* @brief unit_t scale which is linear
* @details Represents units on a linear scale. This is the appropriate unit_t scale for almost
* all units almost all of the time.
* @tparam T underlying storage type
* @sa unit_t
*/
template<typename T>
struct linear_scale
{
inline constexpr linear_scale() = default; ///< default constructor.
inline constexpr linear_scale(const linear_scale&) = default;
inline ~linear_scale() = default;
inline linear_scale& operator=(const linear_scale&) = default;
#if defined(_MSC_VER) && (_MSC_VER > 1800)
inline constexpr linear_scale(linear_scale&&) = default;
inline linear_scale& operator=(linear_scale&&) = default;
#endif
template<class... Args>
inline constexpr linear_scale(const T& value, Args&&...) noexcept : m_value(value) {} ///< constructor.
inline constexpr T operator()() const noexcept { return m_value; } ///< returns value.
T m_value; ///< linearized value.
};
//----------------------------------
// SCALAR (LINEAR) UNITS
//----------------------------------
// Scalar units are the *ONLY* units implicitly convertible to/from built-in types.
namespace dimensionless
{
typedef unit<std::ratio<1>, units::category::scalar_unit> scalar;
typedef unit<std::ratio<1>, units::category::dimensionless_unit> dimensionless;
typedef unit_t<scalar> scalar_t;
typedef scalar_t dimensionless_t;
}
// ignore the redeclaration of the default template parameters
#if defined(_MSC_VER)
# pragma warning(push)
# pragma warning(disable : 4348)
#endif
UNIT_ADD_CATEGORY_TRAIT(scalar)
UNIT_ADD_CATEGORY_TRAIT(dimensionless)
#if defined(_MSC_VER)
# pragma warning(pop)
#endif
//------------------------------
// LINEAR ARITHMETIC
//------------------------------
template<class UnitTypeLhs, class UnitTypeRhs, std::enable_if_t<!traits::is_same_scale<UnitTypeLhs, UnitTypeRhs>::value, int> = 0>
constexpr inline int operator+(const UnitTypeLhs& /* lhs */, const UnitTypeRhs& /* rhs */) noexcept
{
static_assert(traits::is_same_scale<UnitTypeLhs, UnitTypeRhs>::value, "Cannot add units with different linear/non-linear scales.");
return 0;
}
/// Addition operator for unit_t types with a linear_scale.
template<class UnitTypeLhs, class UnitTypeRhs, std::enable_if_t<traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value, int> = 0>
inline constexpr UnitTypeLhs operator+(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept
{
using UnitsLhs = typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type;
using UnitsRhs = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
return UnitTypeLhs(lhs() + convert<UnitsRhs, UnitsLhs>(rhs()));
}
/// Addition operator for scalar unit_t types with a linear_scale. Scalar types can be implicitly converted to built-in types.
template<typename T, std::enable_if_t<std::is_arithmetic<T>::value, int> = 0>
inline constexpr dimensionless::scalar_t operator+(const dimensionless::scalar_t& lhs, T rhs) noexcept
{
return dimensionless::scalar_t(lhs() + rhs);
}
/// Addition operator for scalar unit_t types with a linear_scale. Scalar types can be implicitly converted to built-in types.
template<typename T, std::enable_if_t<std::is_arithmetic<T>::value, int> = 0>
inline constexpr dimensionless::scalar_t operator+(T lhs, const dimensionless::scalar_t& rhs) noexcept
{
return dimensionless::scalar_t(lhs + rhs());
}
/// Subtraction operator for unit_t types with a linear_scale.
template<class UnitTypeLhs, class UnitTypeRhs, std::enable_if_t<traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value, int> = 0>
inline constexpr UnitTypeLhs operator-(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept
{
using UnitsLhs = typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type;
using UnitsRhs = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
return UnitTypeLhs(lhs() - convert<UnitsRhs, UnitsLhs>(rhs()));
}
/// Subtraction operator for scalar unit_t types with a linear_scale. Scalar types can be implicitly converted to built-in types.
template<typename T, std::enable_if_t<std::is_arithmetic<T>::value, int> = 0>
inline constexpr dimensionless::scalar_t operator-(const dimensionless::scalar_t& lhs, T rhs) noexcept
{
return dimensionless::scalar_t(lhs() - rhs);
}
/// Subtraction operator for scalar unit_t types with a linear_scale. Scalar types can be implicitly converted to built-in types.
template<typename T, std::enable_if_t<std::is_arithmetic<T>::value, int> = 0>
inline constexpr dimensionless::scalar_t operator-(T lhs, const dimensionless::scalar_t& rhs) noexcept
{
return dimensionless::scalar_t(lhs - rhs());
}
/// Multiplication type for convertible unit_t types with a linear scale. @returns the multiplied value, with the same type as left-hand side unit.
template<class UnitTypeLhs, class UnitTypeRhs,
std::enable_if_t<traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value && traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value, int> = 0>
inline constexpr auto operator*(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept -> unit_t<compound_unit<squared<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type>>>
{
using UnitsLhs = typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type;
using UnitsRhs = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
return unit_t<compound_unit<squared<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type>>>
(lhs() * convert<UnitsRhs, UnitsLhs>(rhs()));
}
/// Multiplication type for non-convertible unit_t types with a linear scale. @returns the multiplied value, whose type is a compound unit of the left and right hand side values.
template<class UnitTypeLhs, class UnitTypeRhs,
std::enable_if_t<!traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value && traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value && !traits::is_dimensionless_unit<UnitTypeLhs>::value && !traits::is_dimensionless_unit<UnitTypeRhs>::value, int> = 0>
inline constexpr auto operator*(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept -> unit_t<compound_unit<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type, typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type>>
{
using UnitsLhs = typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type;
using UnitsRhs = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
return unit_t<compound_unit<UnitsLhs, UnitsRhs>>
(lhs() * rhs());
}
/// Multiplication by a dimensionless unit for unit_t types with a linear scale.
template<class UnitTypeLhs, typename UnitTypeRhs,
std::enable_if_t<traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value && !traits::is_dimensionless_unit<UnitTypeLhs>::value && traits::is_dimensionless_unit<UnitTypeRhs>::value, int> = 0>
inline constexpr UnitTypeLhs operator*(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept
{
// the cast makes sure factors of PI are handled as expected
return UnitTypeLhs(lhs() * static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs));
}
/// Multiplication by a dimensionless unit for unit_t types with a linear scale.
template<class UnitTypeLhs, typename UnitTypeRhs,
std::enable_if_t<traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value && traits::is_dimensionless_unit<UnitTypeLhs>::value && !traits::is_dimensionless_unit<UnitTypeRhs>::value, int> = 0>
inline constexpr UnitTypeRhs operator*(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept
{
// the cast makes sure factors of PI are handled as expected
return UnitTypeRhs(static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs) * rhs());
}
/// Multiplication by a scalar for unit_t types with a linear scale.
template<class UnitTypeLhs, typename T,
std::enable_if_t<std::is_arithmetic<T>::value && traits::has_linear_scale<UnitTypeLhs>::value, int> = 0>
inline constexpr UnitTypeLhs operator*(const UnitTypeLhs& lhs, T rhs) noexcept
{
return UnitTypeLhs(lhs() * rhs);
}
/// Multiplication by a scalar for unit_t types with a linear scale.
template<class UnitTypeRhs, typename T,
std::enable_if_t<std::is_arithmetic<T>::value && traits::has_linear_scale<UnitTypeRhs>::value, int> = 0>
inline constexpr UnitTypeRhs operator*(T lhs, const UnitTypeRhs& rhs) noexcept
{
return UnitTypeRhs(lhs * rhs());
}
/// Division for convertible unit_t types with a linear scale. @returns the lhs divided by rhs value, whose type is a scalar
template<class UnitTypeLhs, class UnitTypeRhs,
std::enable_if_t<traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value && traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value, int> = 0>
inline constexpr dimensionless::scalar_t operator/(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept
{
using UnitsLhs = typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type;
using UnitsRhs = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
return dimensionless::scalar_t(lhs() / convert<UnitsRhs, UnitsLhs>(rhs()));
}
/// Division for non-convertible unit_t types with a linear scale. @returns the lhs divided by the rhs, with a compound unit type of lhs/rhs
template<class UnitTypeLhs, class UnitTypeRhs,
std::enable_if_t<!traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value && traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value && !traits::is_dimensionless_unit<UnitTypeLhs>::value && !traits::is_dimensionless_unit<UnitTypeRhs>::value, int> = 0>
inline constexpr auto operator/(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept -> unit_t<compound_unit<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type, inverse<typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type>>>
{
using UnitsLhs = typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type;
using UnitsRhs = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
return unit_t<compound_unit<UnitsLhs, inverse<UnitsRhs>>>
(lhs() / rhs());
}
/// Division by a dimensionless unit for unit_t types with a linear scale
template<class UnitTypeLhs, class UnitTypeRhs,
std::enable_if_t<traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value && !traits::is_dimensionless_unit<UnitTypeLhs>::value && traits::is_dimensionless_unit<UnitTypeRhs>::value, int> = 0>
inline constexpr UnitTypeLhs operator/(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept
{
return UnitTypeLhs(lhs() / static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs));
}
/// Division of a dimensionless unit by a unit_t type with a linear scale
template<class UnitTypeLhs, class UnitTypeRhs,
std::enable_if_t<traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value && traits::is_dimensionless_unit<UnitTypeLhs>::value && !traits::is_dimensionless_unit<UnitTypeRhs>::value, int> = 0>
inline constexpr auto operator/(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept -> unit_t<inverse<typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type>>
{
return unit_t<inverse<typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type>>
(static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs) / rhs());
}
/// Division by a scalar for unit_t types with a linear scale
template<class UnitTypeLhs, typename T,
std::enable_if_t<std::is_arithmetic<T>::value && traits::has_linear_scale<UnitTypeLhs>::value, int> = 0>
inline constexpr UnitTypeLhs operator/(const UnitTypeLhs& lhs, T rhs) noexcept
{
return UnitTypeLhs(lhs() / rhs);
}
/// Division of a scalar by a unit_t type with a linear scale
template<class UnitTypeRhs, typename T,
std::enable_if_t<std::is_arithmetic<T>::value && traits::has_linear_scale<UnitTypeRhs>::value, int> = 0>
inline constexpr auto operator/(T lhs, const UnitTypeRhs& rhs) noexcept -> unit_t<inverse<typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type>>
{
using UnitsRhs = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
return unit_t<inverse<UnitsRhs>>
(lhs / rhs());
}
//----------------------------------
// SCALAR COMPARISONS
//----------------------------------
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator==(const UNIT_LIB_DEFAULT_TYPE lhs, const Units& rhs) noexcept
{
return detail::abs(lhs - static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs)) < std::numeric_limits<UNIT_LIB_DEFAULT_TYPE>::epsilon() * detail::abs(lhs + static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs)) ||
detail::abs(lhs - static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs)) < std::numeric_limits<UNIT_LIB_DEFAULT_TYPE>::min();
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator==(const Units& lhs, const UNIT_LIB_DEFAULT_TYPE rhs) noexcept
{
return detail::abs(static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs) - rhs) < std::numeric_limits<UNIT_LIB_DEFAULT_TYPE>::epsilon() * detail::abs(static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs) + rhs) ||
detail::abs(static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs) - rhs) < std::numeric_limits<UNIT_LIB_DEFAULT_TYPE>::min();
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator!=(const UNIT_LIB_DEFAULT_TYPE lhs, const Units& rhs) noexcept
{
return!(lhs == static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs));
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator!=(const Units& lhs, const UNIT_LIB_DEFAULT_TYPE rhs) noexcept
{
return !(static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs) == rhs);
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator>=(const UNIT_LIB_DEFAULT_TYPE lhs, const Units& rhs) noexcept
{
return std::isgreaterequal(lhs, static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs));
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator>=(const Units& lhs, const UNIT_LIB_DEFAULT_TYPE rhs) noexcept
{
return std::isgreaterequal(static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs), rhs);
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator>(const UNIT_LIB_DEFAULT_TYPE lhs, const Units& rhs) noexcept
{
return lhs > static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs);
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator>(const Units& lhs, const UNIT_LIB_DEFAULT_TYPE rhs) noexcept
{
return static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs) > rhs;
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator<=(const UNIT_LIB_DEFAULT_TYPE lhs, const Units& rhs) noexcept
{
return std::islessequal(lhs, static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs));
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator<=(const Units& lhs, const UNIT_LIB_DEFAULT_TYPE rhs) noexcept
{
return std::islessequal(static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs), rhs);
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator<(const UNIT_LIB_DEFAULT_TYPE lhs, const Units& rhs) noexcept
{
return lhs < static_cast<UNIT_LIB_DEFAULT_TYPE>(rhs);
}
template<typename Units, class = std::enable_if_t<units::traits::is_dimensionless_unit<Units>::value>>
constexpr bool operator<(const Units& lhs, const UNIT_LIB_DEFAULT_TYPE rhs) noexcept
{
return static_cast<UNIT_LIB_DEFAULT_TYPE>(lhs) < rhs;
}
//----------------------------------
// POW
//----------------------------------
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
/// recursive exponential implementation
template <int N, class U> struct power_of_unit
{
typedef typename units::detail::unit_multiply<U, typename power_of_unit<N - 1, U>::type> type;
};
/// End recursion
template <class U> struct power_of_unit<1, U>
{
typedef U type;
};
}
/** @endcond */ // END DOXYGEN IGNORE
namespace math
{
/**
* @brief computes the value of <i>value</i> raised to the <i>power</i>
* @details Only implemented for linear_scale units. <i>Power</i> must be known at compile time, so the resulting unit type can be deduced.
* @tparam power exponential power to raise <i>value</i> by.
* @param[in] value `unit_t` derived type to raise to the given <i>power</i>
* @returns new unit_t, raised to the given exponent
*/
template<int power, class UnitType, class = typename std::enable_if<traits::has_linear_scale<UnitType>::value, int>>
inline auto pow(const UnitType& value) noexcept -> unit_t<typename units::detail::power_of_unit<power, typename units::traits::unit_t_traits<UnitType>::unit_type>::type, typename units::traits::unit_t_traits<UnitType>::underlying_type, linear_scale>
{
return unit_t<typename units::detail::power_of_unit<power, typename units::traits::unit_t_traits<UnitType>::unit_type>::type, typename units::traits::unit_t_traits<UnitType>::underlying_type, linear_scale>
(std::pow(value(), power));
}
/**
* @brief computes the value of <i>value</i> raised to the <i>power</i> as a constexpr
* @details Only implemented for linear_scale units. <i>Power</i> must be known at compile time, so the resulting unit type can be deduced.
* Additionally, the power must be <i>a positive, integral, value</i>.
* @tparam power exponential power to raise <i>value</i> by.
* @param[in] value `unit_t` derived type to raise to the given <i>power</i>
* @returns new unit_t, raised to the given exponent
*/
template<int power, class UnitType, class = typename std::enable_if<traits::has_linear_scale<UnitType>::value, int>>
inline constexpr auto cpow(const UnitType& value) noexcept -> unit_t<typename units::detail::power_of_unit<power, typename units::traits::unit_t_traits<UnitType>::unit_type>::type, typename units::traits::unit_t_traits<UnitType>::underlying_type, linear_scale>
{
static_assert(power >= 0, "cpow cannot accept negative numbers. Try units::math::pow instead.");
return unit_t<typename units::detail::power_of_unit<power, typename units::traits::unit_t_traits<UnitType>::unit_type>::type, typename units::traits::unit_t_traits<UnitType>::underlying_type, linear_scale>
(detail::pow(value(), power));
}
}
//------------------------------
// DECIBEL SCALE
//------------------------------
/**
* @brief unit_t scale for representing decibel values.
* @details internally stores linearized values. `operator()` returns the value in dB.
* @tparam T underlying storage type
* @sa unit_t
*/
template<typename T>
struct decibel_scale
{
inline constexpr decibel_scale() = default;
inline constexpr decibel_scale(const decibel_scale&) = default;
inline ~decibel_scale() = default;
inline decibel_scale& operator=(const decibel_scale&) = default;
#if defined(_MSC_VER) && (_MSC_VER > 1800)
inline constexpr decibel_scale(decibel_scale&&) = default;
inline decibel_scale& operator=(decibel_scale&&) = default;
#endif
inline constexpr decibel_scale(const T value) noexcept : m_value(std::pow(10, value / 10)) {}
template<class... Args>
inline constexpr decibel_scale(const T value, std::true_type, Args&&...) noexcept : m_value(value) {}
inline constexpr T operator()() const noexcept { return 10 * std::log10(m_value); }
T m_value; ///< linearized value
};
//------------------------------
// SCALAR (DECIBEL) UNITS
//------------------------------
/**
* @brief namespace for unit types and containers for units that have no dimension (scalar units)
* @sa See unit_t for more information on unit type containers.
*/
namespace dimensionless
{
typedef unit_t<scalar, UNIT_LIB_DEFAULT_TYPE, decibel_scale> dB_t;
#if !defined(UNIT_LIB_DISABLE_IOSTREAM)
inline std::ostream& operator<<(std::ostream& os, const dB_t& obj) { os << obj() << " dB"; return os; }
#endif
typedef dB_t dBi_t;
}
//------------------------------
// DECIBEL ARITHMETIC
//------------------------------
/// Addition for convertible unit_t types with a decibel_scale
template<class UnitTypeLhs, class UnitTypeRhs,
std::enable_if_t<traits::has_decibel_scale<UnitTypeLhs, UnitTypeRhs>::value, int> = 0>
constexpr inline auto operator+(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept -> unit_t<compound_unit<squared<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type>>, typename units::traits::unit_t_traits<UnitTypeLhs>::underlying_type, decibel_scale>
{
using LhsUnits = typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type;
using RhsUnits = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
using underlying_type = typename units::traits::unit_t_traits<UnitTypeLhs>::underlying_type;
return unit_t<compound_unit<squared<LhsUnits>>, underlying_type, decibel_scale>
(lhs.template toLinearized<underlying_type>() * convert<RhsUnits, LhsUnits>(rhs.template toLinearized<underlying_type>()), std::true_type());
}
/// Addition between unit_t types with a decibel_scale and dimensionless dB units
template<class UnitTypeLhs, std::enable_if_t<traits::has_decibel_scale<UnitTypeLhs>::value && !traits::is_dimensionless_unit<UnitTypeLhs>::value, int> = 0>
constexpr inline UnitTypeLhs operator+(const UnitTypeLhs& lhs, const dimensionless::dB_t& rhs) noexcept
{
using underlying_type = typename units::traits::unit_t_traits<UnitTypeLhs>::underlying_type;
return UnitTypeLhs(lhs.template toLinearized<underlying_type>() * rhs.template toLinearized<underlying_type>(), std::true_type());
}
/// Addition between unit_t types with a decibel_scale and dimensionless dB units
template<class UnitTypeRhs, std::enable_if_t<traits::has_decibel_scale<UnitTypeRhs>::value && !traits::is_dimensionless_unit<UnitTypeRhs>::value, int> = 0>
constexpr inline UnitTypeRhs operator+(const dimensionless::dB_t& lhs, const UnitTypeRhs& rhs) noexcept
{
using underlying_type = typename units::traits::unit_t_traits<UnitTypeRhs>::underlying_type;
return UnitTypeRhs(lhs.template toLinearized<underlying_type>() * rhs.template toLinearized<underlying_type>(), std::true_type());
}
/// Subtraction for convertible unit_t types with a decibel_scale
template<class UnitTypeLhs, class UnitTypeRhs, std::enable_if_t<traits::has_decibel_scale<UnitTypeLhs, UnitTypeRhs>::value, int> = 0>
constexpr inline auto operator-(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs) noexcept -> unit_t<compound_unit<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type, inverse<typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type>>, typename units::traits::unit_t_traits<UnitTypeLhs>::underlying_type, decibel_scale>
{
using LhsUnits = typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type;
using RhsUnits = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
using underlying_type = typename units::traits::unit_t_traits<UnitTypeLhs>::underlying_type;
return unit_t<compound_unit<LhsUnits, inverse<RhsUnits>>, underlying_type, decibel_scale>
(lhs.template toLinearized<underlying_type>() / convert<RhsUnits, LhsUnits>(rhs.template toLinearized<underlying_type>()), std::true_type());
}
/// Subtraction between unit_t types with a decibel_scale and dimensionless dB units
template<class UnitTypeLhs, std::enable_if_t<traits::has_decibel_scale<UnitTypeLhs>::value && !traits::is_dimensionless_unit<UnitTypeLhs>::value, int> = 0>
constexpr inline UnitTypeLhs operator-(const UnitTypeLhs& lhs, const dimensionless::dB_t& rhs) noexcept
{
using underlying_type = typename units::traits::unit_t_traits<UnitTypeLhs>::underlying_type;
return UnitTypeLhs(lhs.template toLinearized<underlying_type>() / rhs.template toLinearized<underlying_type>(), std::true_type());
}
/// Subtraction between unit_t types with a decibel_scale and dimensionless dB units
template<class UnitTypeRhs, std::enable_if_t<traits::has_decibel_scale<UnitTypeRhs>::value && !traits::is_dimensionless_unit<UnitTypeRhs>::value, int> = 0>
constexpr inline auto operator-(const dimensionless::dB_t& lhs, const UnitTypeRhs& rhs) noexcept -> unit_t<inverse<typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type>, typename units::traits::unit_t_traits<UnitTypeRhs>::underlying_type, decibel_scale>
{
using RhsUnits = typename units::traits::unit_t_traits<UnitTypeRhs>::unit_type;
using underlying_type = typename units::traits::unit_t_traits<RhsUnits>::underlying_type;
return unit_t<inverse<RhsUnits>, underlying_type, decibel_scale>
(lhs.template toLinearized<underlying_type>() / rhs.template toLinearized<underlying_type>(), std::true_type());
}
//----------------------------------
// UNIT RATIO CLASS
//----------------------------------
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
template<class Units>
struct _unit_value_t {};
}
/** @endcond */ // END DOXYGEN IGNORE
namespace traits
{
#ifdef FOR_DOXYGEN_PURPOSES_ONLY
/**
* @ingroup TypeTraits
* @brief Trait for accessing the publically defined types of `units::unit_value_t_traits`
* @details The units library determines certain properties of the `unit_value_t` types passed to
* them and what they represent by using the members of the corresponding `unit_value_t_traits`
* instantiation.
*/
template<typename T>
struct unit_value_t_traits
{
typedef typename T::unit_type unit_type; ///< Dimension represented by the `unit_value_t`.
typedef typename T::ratio ratio; ///< Quantity represented by the `unit_value_t`, expressed as arational number.
};
#endif
/** @cond */ // DOXYGEN IGNORE
/**
* @brief unit_value_t_traits specialization for things which are not unit_t
* @details
*/
template<typename T, typename = void>
struct unit_value_t_traits
{
typedef void unit_type;
typedef void ratio;
};
/**
* @ingroup TypeTraits
* @brief Trait for accessing the publically defined types of `units::unit_value_t_traits`
* @details
*/
template<typename T>
struct unit_value_t_traits <T, typename void_t<
typename T::unit_type,
typename T::ratio>::type>
{
typedef typename T::unit_type unit_type;
typedef typename T::ratio ratio;
};
/** @endcond */ // END DOXYGEN IGNORE
}
//------------------------------------------------------------------------------
// COMPILE-TIME UNIT VALUES AND ARITHMETIC
//------------------------------------------------------------------------------
/**
* @ingroup UnitContainers
* @brief Stores a rational unit value as a compile-time constant
* @details unit_value_t is useful for performing compile-time arithmetic on known
* unit quantities.
* @tparam Units units represented by the `unit_value_t`
* @tparam Num numerator of the represented value.
* @tparam Denom denominator of the represented value.
* @sa unit_value_t_traits to access information about the properties of the class,
* such as it's unit type and rational value.
* @note This is intentionally identical in concept to a `std::ratio`.
*
*/
template<typename Units, std::uintmax_t Num, std::uintmax_t Denom = 1>
struct unit_value_t : units::detail::_unit_value_t<Units>
{
typedef Units unit_type;
typedef std::ratio<Num, Denom> ratio;
static_assert(traits::is_unit<Units>::value, "Template parameter `Units` must be a unit type.");
static constexpr const unit_t<Units> value() { return unit_t<Units>((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den); }
};
namespace traits
{
/**
* @ingroup TypeTraits
* @brief Trait which tests whether a type is a unit_value_t representing the given unit type.
* @details e.g. `is_unit_value_t<meters, myType>::value` would test that `myType` is a
* `unit_value_t<meters>`.
* @tparam Units units that the `unit_value_t` is supposed to have.
* @tparam T type to test.
*/
template<typename T, typename Units = typename traits::unit_value_t_traits<T>::unit_type>
struct is_unit_value_t : std::integral_constant<bool,
std::is_base_of<units::detail::_unit_value_t<Units>, T>::value>
{};
/**
* @ingroup TypeTraits
* @brief Trait which tests whether type T is a unit_value_t with a unit type in the given category.
* @details e.g. `is_unit_value_t_category<units::category::length, unit_value_t<feet>>::value` would be true
*/
template<typename Category, typename T>
struct is_unit_value_t_category : std::integral_constant<bool,
std::is_same<units::traits::base_unit_of<typename traits::unit_value_t_traits<T>::unit_type>, Category>::value>
{
static_assert(is_base_unit<Category>::value, "Template parameter `Category` must be a `base_unit` type.");
};
}
/** @cond */ // DOXYGEN IGNORE
namespace detail
{
// base class for common arithmetic
template<class U1, class U2>
struct unit_value_arithmetic
{
static_assert(traits::is_unit_value_t<U1>::value, "Template parameter `U1` must be a `unit_value_t` type.");
static_assert(traits::is_unit_value_t<U2>::value, "Template parameter `U2` must be a `unit_value_t` type.");
using _UNIT1 = typename traits::unit_value_t_traits<U1>::unit_type;
using _UNIT2 = typename traits::unit_value_t_traits<U2>::unit_type;
using _CONV1 = typename units::traits::unit_traits<_UNIT1>::conversion_ratio;
using _CONV2 = typename units::traits::unit_traits<_UNIT2>::conversion_ratio;
using _RATIO1 = typename traits::unit_value_t_traits<U1>::ratio;
using _RATIO2 = typename traits::unit_value_t_traits<U2>::ratio;
using _RATIO2CONV = typename std::ratio_divide<std::ratio_multiply<_RATIO2, _CONV2>, _CONV1>;
using _PI_EXP = std::ratio_subtract<typename units::traits::unit_traits<_UNIT2>::pi_exponent_ratio, typename units::traits::unit_traits<_UNIT1>::pi_exponent_ratio>;
};
}
/** @endcond */ // END DOXYGEN IGNORE
/**
* @ingroup CompileTimeUnitManipulators
* @brief adds two unit_value_t types at compile-time
* @details The resulting unit will the the `unit_type` of `U1`
* @tparam U1 left-hand `unit_value_t`
* @tparam U2 right-hand `unit_value_t`
* @sa unit_value_t_traits to access information about the properties of the class,
* such as it's unit type and rational value.
* @note very similar in concept to `std::ratio_add`
*/
template<class U1, class U2>
struct unit_value_add : units::detail::unit_value_arithmetic<U1, U2>, units::detail::_unit_value_t<typename traits::unit_value_t_traits<U1>::unit_type>
{
/** @cond */ // DOXYGEN IGNORE
using Base = units::detail::unit_value_arithmetic<U1, U2>;
typedef typename Base::_UNIT1 unit_type;
using ratio = std::ratio_add<typename Base::_RATIO1, typename Base::_RATIO2CONV>;
static_assert(traits::is_convertible_unit<typename Base::_UNIT1, typename Base::_UNIT2>::value, "Unit types are not compatible.");
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief Value of sum
* @details Returns the calculated value of the sum of `U1` and `U2`, in the same
* units as `U1`.
* @returns Value of the sum in the appropriate units.
*/
static constexpr const unit_t<unit_type> value() noexcept
{
using UsePi = std::integral_constant<bool, Base::_PI_EXP::num != 0>;
return value(UsePi());
}
/** @cond */ // DOXYGEN IGNORE
// value if PI isn't involved
static constexpr const unit_t<unit_type> value(std::false_type) noexcept
{
return unit_t<unit_type>((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den);
}
// value if PI *is* involved
static constexpr const unit_t<unit_type> value(std::true_type) noexcept
{
return unit_t<unit_type>(((UNIT_LIB_DEFAULT_TYPE)Base::_RATIO1::num / Base::_RATIO1::den) +
((UNIT_LIB_DEFAULT_TYPE)Base::_RATIO2CONV::num / Base::_RATIO2CONV::den) * std::pow(units::constants::detail::PI_VAL, ((UNIT_LIB_DEFAULT_TYPE)Base::_PI_EXP::num / Base::_PI_EXP::den)));
}
/** @endcond */ // END DOXYGEN IGNORE
};
/**
* @ingroup CompileTimeUnitManipulators
* @brief subtracts two unit_value_t types at compile-time
* @details The resulting unit will the the `unit_type` of `U1`
* @tparam U1 left-hand `unit_value_t`
* @tparam U2 right-hand `unit_value_t`
* @sa unit_value_t_traits to access information about the properties of the class,
* such as it's unit type and rational value.
* @note very similar in concept to `std::ratio_subtract`
*/
template<class U1, class U2>
struct unit_value_subtract : units::detail::unit_value_arithmetic<U1, U2>, units::detail::_unit_value_t<typename traits::unit_value_t_traits<U1>::unit_type>
{
/** @cond */ // DOXYGEN IGNORE
using Base = units::detail::unit_value_arithmetic<U1, U2>;
typedef typename Base::_UNIT1 unit_type;
using ratio = std::ratio_subtract<typename Base::_RATIO1, typename Base::_RATIO2CONV>;
static_assert(traits::is_convertible_unit<typename Base::_UNIT1, typename Base::_UNIT2>::value, "Unit types are not compatible.");
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief Value of difference
* @details Returns the calculated value of the difference of `U1` and `U2`, in the same
* units as `U1`.
* @returns Value of the difference in the appropriate units.
*/
static constexpr const unit_t<unit_type> value() noexcept
{
using UsePi = std::integral_constant<bool, Base::_PI_EXP::num != 0>;
return value(UsePi());
}
/** @cond */ // DOXYGEN IGNORE
// value if PI isn't involved
static constexpr const unit_t<unit_type> value(std::false_type) noexcept
{
return unit_t<unit_type>((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den);
}
// value if PI *is* involved
static constexpr const unit_t<unit_type> value(std::true_type) noexcept
{
return unit_t<unit_type>(((UNIT_LIB_DEFAULT_TYPE)Base::_RATIO1::num / Base::_RATIO1::den) - ((UNIT_LIB_DEFAULT_TYPE)Base::_RATIO2CONV::num / Base::_RATIO2CONV::den)
* std::pow(units::constants::detail::PI_VAL, ((UNIT_LIB_DEFAULT_TYPE)Base::_PI_EXP::num / Base::_PI_EXP::den)));
}
/** @endcond */ // END DOXYGEN IGNORE };
};
/**
* @ingroup CompileTimeUnitManipulators
* @brief multiplies two unit_value_t types at compile-time
* @details The resulting unit will the the `unit_type` of `U1 * U2`
* @tparam U1 left-hand `unit_value_t`
* @tparam U2 right-hand `unit_value_t`
* @sa unit_value_t_traits to access information about the properties of the class,
* such as it's unit type and rational value.
* @note very similar in concept to `std::ratio_multiply`
*/
template<class U1, class U2>
struct unit_value_multiply : units::detail::unit_value_arithmetic<U1, U2>,
units::detail::_unit_value_t<typename std::conditional<traits::is_convertible_unit<typename traits::unit_value_t_traits<U1>::unit_type,
typename traits::unit_value_t_traits<U2>::unit_type>::value, compound_unit<squared<typename traits::unit_value_t_traits<U1>::unit_type>>,
compound_unit<typename traits::unit_value_t_traits<U1>::unit_type, typename traits::unit_value_t_traits<U2>::unit_type>>::type>
{
/** @cond */ // DOXYGEN IGNORE
using Base = units::detail::unit_value_arithmetic<U1, U2>;
using unit_type = std::conditional_t<traits::is_convertible_unit<typename Base::_UNIT1, typename Base::_UNIT2>::value, compound_unit<squared<typename Base::_UNIT1>>, compound_unit<typename Base::_UNIT1, typename Base::_UNIT2>>;
using ratio = std::conditional_t<traits::is_convertible_unit<typename Base::_UNIT1, typename Base::_UNIT2>::value, std::ratio_multiply<typename Base::_RATIO1, typename Base::_RATIO2CONV>, std::ratio_multiply<typename Base::_RATIO1, typename Base::_RATIO2>>;
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief Value of product
* @details Returns the calculated value of the product of `U1` and `U2`, in units
* of `U1 x U2`.
* @returns Value of the product in the appropriate units.
*/
static constexpr const unit_t<unit_type> value() noexcept
{
using UsePi = std::integral_constant<bool, Base::_PI_EXP::num != 0>;
return value(UsePi());
}
/** @cond */ // DOXYGEN IGNORE
// value if PI isn't involved
static constexpr const unit_t<unit_type> value(std::false_type) noexcept
{
return unit_t<unit_type>((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den);
}
// value if PI *is* involved
static constexpr const unit_t<unit_type> value(std::true_type) noexcept
{
return unit_t<unit_type>(((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den) * std::pow(units::constants::detail::PI_VAL, ((UNIT_LIB_DEFAULT_TYPE)Base::_PI_EXP::num / Base::_PI_EXP::den)));
}
/** @endcond */ // END DOXYGEN IGNORE
};
/**
* @ingroup CompileTimeUnitManipulators
* @brief divides two unit_value_t types at compile-time
* @details The resulting unit will the the `unit_type` of `U1`
* @tparam U1 left-hand `unit_value_t`
* @tparam U2 right-hand `unit_value_t`
* @sa unit_value_t_traits to access information about the properties of the class,
* such as it's unit type and rational value.
* @note very similar in concept to `std::ratio_divide`
*/
template<class U1, class U2>
struct unit_value_divide : units::detail::unit_value_arithmetic<U1, U2>,
units::detail::_unit_value_t<typename std::conditional<traits::is_convertible_unit<typename traits::unit_value_t_traits<U1>::unit_type,
typename traits::unit_value_t_traits<U2>::unit_type>::value, dimensionless::scalar, compound_unit<typename traits::unit_value_t_traits<U1>::unit_type,
inverse<typename traits::unit_value_t_traits<U2>::unit_type>>>::type>
{
/** @cond */ // DOXYGEN IGNORE
using Base = units::detail::unit_value_arithmetic<U1, U2>;
using unit_type = std::conditional_t<traits::is_convertible_unit<typename Base::_UNIT1, typename Base::_UNIT2>::value, dimensionless::scalar, compound_unit<typename Base::_UNIT1, inverse<typename Base::_UNIT2>>>;
using ratio = std::conditional_t<traits::is_convertible_unit<typename Base::_UNIT1, typename Base::_UNIT2>::value, std::ratio_divide<typename Base::_RATIO1, typename Base::_RATIO2CONV>, std::ratio_divide<typename Base::_RATIO1, typename Base::_RATIO2>>;
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief Value of quotient
* @details Returns the calculated value of the quotient of `U1` and `U2`, in units
* of `U1 x U2`.
* @returns Value of the quotient in the appropriate units.
*/
static constexpr const unit_t<unit_type> value() noexcept
{
using UsePi = std::integral_constant<bool, Base::_PI_EXP::num != 0>;
return value(UsePi());
}
/** @cond */ // DOXYGEN IGNORE
// value if PI isn't involved
static constexpr const unit_t<unit_type> value(std::false_type) noexcept
{
return unit_t<unit_type>((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den);
}
// value if PI *is* involved
static constexpr const unit_t<unit_type> value(std::true_type) noexcept
{
return unit_t<unit_type>(((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den) * std::pow(units::constants::detail::PI_VAL, ((UNIT_LIB_DEFAULT_TYPE)Base::_PI_EXP::num / Base::_PI_EXP::den)));
}
/** @endcond */ // END DOXYGEN IGNORE
};
/**
* @ingroup CompileTimeUnitManipulators
* @brief raises unit_value_to a power at compile-time
* @details The resulting unit will the `unit_type` of `U1` squared
* @tparam U1 `unit_value_t` to take the exponentiation of.
* @sa unit_value_t_traits to access information about the properties of the class,
* such as it's unit type and rational value.
* @note very similar in concept to `units::math::pow`
*/
template<class U1, int power>
struct unit_value_power : units::detail::unit_value_arithmetic<U1, U1>, units::detail::_unit_value_t<typename units::detail::power_of_unit<power, typename traits::unit_value_t_traits<U1>::unit_type>::type>
{
/** @cond */ // DOXYGEN IGNORE
using Base = units::detail::unit_value_arithmetic<U1, U1>;
using unit_type = typename units::detail::power_of_unit<power, typename Base::_UNIT1>::type;
using ratio = typename units::detail::power_of_ratio<power, typename Base::_RATIO1>::type;
using pi_exponent = std::ratio_multiply<std::ratio<power>, typename Base::_UNIT1::pi_exponent_ratio>;
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief Value of exponentiation
* @details Returns the calculated value of the exponentiation of `U1`, in units
* of `U1^power`.
* @returns Value of the exponentiation in the appropriate units.
*/
static constexpr const unit_t<unit_type> value() noexcept
{
using UsePi = std::integral_constant<bool, Base::_PI_EXP::num != 0>;
return value(UsePi());
}
/** @cond */ // DOXYGEN IGNORE
// value if PI isn't involved
static constexpr const unit_t<unit_type> value(std::false_type) noexcept
{
return unit_t<unit_type>((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den);
}
// value if PI *is* involved
static constexpr const unit_t<unit_type> value(std::true_type) noexcept
{
return unit_t<unit_type>(((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den) * std::pow(units::constants::detail::PI_VAL, ((UNIT_LIB_DEFAULT_TYPE)pi_exponent::num / pi_exponent::den)));
}
/** @endcond */ // END DOXYGEN IGNORE };
};
/**
* @ingroup CompileTimeUnitManipulators
* @brief calculates square root of unit_value_t at compile-time
* @details The resulting unit will the square root `unit_type` of `U1`
* @tparam U1 `unit_value_t` to take the square root of.
* @sa unit_value_t_traits to access information about the properties of the class,
* such as it's unit type and rational value.
* @note very similar in concept to `units::ratio_sqrt`
*/
template<class U1, std::intmax_t Eps = 10000000000>
struct unit_value_sqrt : units::detail::unit_value_arithmetic<U1, U1>, units::detail::_unit_value_t<square_root<typename traits::unit_value_t_traits<U1>::unit_type, Eps>>
{
/** @cond */ // DOXYGEN IGNORE
using Base = units::detail::unit_value_arithmetic<U1, U1>;
using unit_type = square_root<typename Base::_UNIT1, Eps>;
using ratio = ratio_sqrt<typename Base::_RATIO1, Eps>;
using pi_exponent = ratio_sqrt<typename Base::_UNIT1::pi_exponent_ratio, Eps>;
/** @endcond */ // END DOXYGEN IGNORE
/**
* @brief Value of square root
* @details Returns the calculated value of the square root of `U1`, in units
* of `U1^1/2`.
* @returns Value of the square root in the appropriate units.
*/
static constexpr const unit_t<unit_type> value() noexcept
{
using UsePi = std::integral_constant<bool, Base::_PI_EXP::num != 0>;
return value(UsePi());
}
/** @cond */ // DOXYGEN IGNORE
// value if PI isn't involved
static constexpr const unit_t<unit_type> value(std::false_type) noexcept
{
return unit_t<unit_type>((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den);
}
// value if PI *is* involved
static constexpr const unit_t<unit_type> value(std::true_type) noexcept
{
return unit_t<unit_type>(((UNIT_LIB_DEFAULT_TYPE)ratio::num / ratio::den) * std::pow(units::constants::detail::PI_VAL, ((UNIT_LIB_DEFAULT_TYPE)pi_exponent::num / pi_exponent::den)));
}
/** @endcond */ // END DOXYGEN IGNORE
};
//------------------------------
// LITERALS
//------------------------------
/**
* @namespace units::literals
* @brief namespace for unit literal definitions of all categories.
* @details Literals allow for declaring unit types using suffix values. For example, a type
* of `meter_t(6.2)` could be declared as `6.2_m`. All literals use an underscore
* followed by the abbreviation for the unit. To enable literal syntax in your code,
* include the statement `using namespace units::literals`.
* @anchor unitLiterals
* @sa See unit_t for more information on unit type containers.
*/
//------------------------------
// LENGTH UNITS
//------------------------------
/**
* @namespace units::length
* @brief namespace for unit types and containers representing length values
* @details The SI unit for length is `meters`, and the corresponding `base_unit` category is
* `length_unit`.
* @anchor lengthContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_LENGTH_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(length, meter, meters, m, unit<std::ratio<1>, units::category::length_unit>)
UNIT_ADD(length, foot, feet, ft, unit<std::ratio<381, 1250>, meters>)
UNIT_ADD(length, mil, mils, mil, unit<std::ratio<1000>, feet>)
UNIT_ADD(length, inch, inches, in, unit<std::ratio<1, 12>, feet>)
UNIT_ADD(length, mile, miles, mi, unit<std::ratio<5280>, feet>)
UNIT_ADD(length, nauticalMile, nauticalMiles, nmi, unit<std::ratio<1852>, meters>)
UNIT_ADD(length, astronicalUnit, astronicalUnits, au, unit<std::ratio<149597870700>, meters>)
UNIT_ADD(length, lightyear, lightyears, ly, unit<std::ratio<9460730472580800>, meters>)
UNIT_ADD(length, parsec, parsecs, pc, unit<std::ratio<648000>, astronicalUnits, std::ratio<-1>>)
UNIT_ADD(length, angstrom, angstroms, angstrom, unit<std::ratio<1, 10>, nanometers>)
UNIT_ADD(length, cubit, cubits, cbt, unit<std::ratio<18>, inches>)
UNIT_ADD(length, fathom, fathoms, ftm, unit<std::ratio<6>, feet>)
UNIT_ADD(length, chain, chains, ch, unit<std::ratio<66>, feet>)
UNIT_ADD(length, furlong, furlongs, fur, unit<std::ratio<10>, chains>)
UNIT_ADD(length, hand, hands, hand, unit<std::ratio<4>, inches>)
UNIT_ADD(length, league, leagues, lea, unit<std::ratio<3>, miles>)
UNIT_ADD(length, nauticalLeague, nauticalLeagues, nl, unit<std::ratio<3>, nauticalMiles>)
UNIT_ADD(length, yard, yards, yd, unit<std::ratio<3>, feet>)
UNIT_ADD_CATEGORY_TRAIT(length)
#endif
//------------------------------
// MASS UNITS
//------------------------------
/**
* @namespace units::mass
* @brief namespace for unit types and containers representing mass values
* @details The SI unit for mass is `kilograms`, and the corresponding `base_unit` category is
* `mass_unit`.
* @anchor massContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_MASS_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(mass, gram, grams, g, unit<std::ratio<1, 1000>, units::category::mass_unit>)
UNIT_ADD(mass, metric_ton, metric_tons, t, unit<std::ratio<1000>, kilograms>)
UNIT_ADD(mass, pound, pounds, lb, unit<std::ratio<45359237, 100000000>, kilograms>)
UNIT_ADD(mass, long_ton, long_tons, ln_t, unit<std::ratio<2240>, pounds>)
UNIT_ADD(mass, short_ton, short_tons, sh_t, unit<std::ratio<2000>, pounds>)
UNIT_ADD(mass, stone, stone, st, unit<std::ratio<14>, pounds>)
UNIT_ADD(mass, ounce, ounces, oz, unit<std::ratio<1, 16>, pounds>)
UNIT_ADD(mass, carat, carats, ct, unit<std::ratio<200>, milligrams>)
UNIT_ADD(mass, slug, slugs, slug, unit<std::ratio<145939029, 10000000>, kilograms>)
UNIT_ADD_CATEGORY_TRAIT(mass)
#endif
//------------------------------
// TIME UNITS
//------------------------------
/**
* @namespace units::time
* @brief namespace for unit types and containers representing time values
* @details The SI unit for time is `seconds`, and the corresponding `base_unit` category is
* `time_unit`.
* @anchor timeContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_TIME_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(time, second, seconds, s, unit<std::ratio<1>, units::category::time_unit>)
UNIT_ADD(time, minute, minutes, min, unit<std::ratio<60>, seconds>)
UNIT_ADD(time, hour, hours, hr, unit<std::ratio<60>, minutes>)
UNIT_ADD(time, day, days, d, unit<std::ratio<24>, hours>)
UNIT_ADD(time, week, weeks, wk, unit<std::ratio<7>, days>)
UNIT_ADD(time, year, years, yr, unit<std::ratio<365>, days>)
UNIT_ADD(time, julian_year, julian_years, a_j, unit<std::ratio<31557600>, seconds>)
UNIT_ADD(time, gregorian_year, gregorian_years, a_g, unit<std::ratio<31556952>, seconds>)
UNIT_ADD_CATEGORY_TRAIT(time)
#endif
//------------------------------
// ANGLE UNITS
//------------------------------
/**
* @namespace units::angle
* @brief namespace for unit types and containers representing angle values
* @details The SI unit for angle is `radians`, and the corresponding `base_unit` category is
* `angle_unit`.
* @anchor angleContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(angle, radian, radians, rad, unit<std::ratio<1>, units::category::angle_unit>)
UNIT_ADD(angle, degree, degrees, deg, unit<std::ratio<1, 180>, radians, std::ratio<1>>)
UNIT_ADD(angle, arcminute, arcminutes, arcmin, unit<std::ratio<1, 60>, degrees>)
UNIT_ADD(angle, arcsecond, arcseconds, arcsec, unit<std::ratio<1, 60>, arcminutes>)
UNIT_ADD(angle, milliarcsecond, milliarcseconds, mas, milli<arcseconds>)
UNIT_ADD(angle, turn, turns, tr, unit<std::ratio<2>, radians, std::ratio<1>>)
UNIT_ADD(angle, gradian, gradians, gon, unit<std::ratio<1, 400>, turns>)
UNIT_ADD_CATEGORY_TRAIT(angle)
#endif
//------------------------------
// UNITS OF CURRENT
//------------------------------
/**
* @namespace units::current
* @brief namespace for unit types and containers representing current values
* @details The SI unit for current is `amperes`, and the corresponding `base_unit` category is
* `current_unit`.
* @anchor currentContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_CURRENT_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(current, ampere, amperes, A, unit<std::ratio<1>, units::category::current_unit>)
UNIT_ADD_CATEGORY_TRAIT(current)
#endif
//------------------------------
// UNITS OF TEMPERATURE
//------------------------------
// NOTE: temperature units have special conversion overloads, since they
// require translations and aren't a reversible transform.
/**
* @namespace units::temperature
* @brief namespace for unit types and containers representing temperature values
* @details The SI unit for temperature is `kelvin`, and the corresponding `base_unit` category is
* `temperature_unit`.
* @anchor temperatureContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_TEMPERATURE_UNITS)
UNIT_ADD(temperature, kelvin, kelvin, K, unit<std::ratio<1>, units::category::temperature_unit>)
UNIT_ADD(temperature, celsius, celsius, degC, unit<std::ratio<1>, kelvin, std::ratio<0>, std::ratio<27315, 100>>)
UNIT_ADD(temperature, fahrenheit, fahrenheit, degF, unit<std::ratio<5, 9>, celsius, std::ratio<0>, std::ratio<-160, 9>>)
UNIT_ADD(temperature, reaumur, reaumur, Re, unit<std::ratio<10, 8>, celsius>)
UNIT_ADD(temperature, rankine, rankine, Ra, unit<std::ratio<5, 9>, kelvin>)
UNIT_ADD_CATEGORY_TRAIT(temperature)
#endif
//------------------------------
// UNITS OF AMOUNT OF SUBSTANCE
//------------------------------
/**
* @namespace units::substance
* @brief namespace for unit types and containers representing substance values
* @details The SI unit for substance is `moles`, and the corresponding `base_unit` category is
* `substance_unit`.
* @anchor substanceContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_SUBSTANCE_UNITS)
UNIT_ADD(substance, mole, moles, mol, unit<std::ratio<1>, units::category::substance_unit>)
UNIT_ADD_CATEGORY_TRAIT(substance)
#endif
//------------------------------
// UNITS OF LUMINOUS INTENSITY
//------------------------------
/**
* @namespace units::luminous_intensity
* @brief namespace for unit types and containers representing luminous_intensity values
* @details The SI unit for luminous_intensity is `candelas`, and the corresponding `base_unit` category is
* `luminous_intensity_unit`.
* @anchor luminousIntensityContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_LUMINOUS_INTENSITY_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(luminous_intensity, candela, candelas, cd, unit<std::ratio<1>, units::category::luminous_intensity_unit>)
UNIT_ADD_CATEGORY_TRAIT(luminous_intensity)
#endif
//------------------------------
// UNITS OF SOLID ANGLE
//------------------------------
/**
* @namespace units::solid_angle
* @brief namespace for unit types and containers representing solid_angle values
* @details The SI unit for solid_angle is `steradians`, and the corresponding `base_unit` category is
* `solid_angle_unit`.
* @anchor solidAngleContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_SOLID_ANGLE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(solid_angle, steradian, steradians, sr, unit<std::ratio<1>, units::category::solid_angle_unit>)
UNIT_ADD(solid_angle, degree_squared, degrees_squared, sq_deg, squared<angle::degrees>)
UNIT_ADD(solid_angle, spat, spats, sp, unit<std::ratio<4>, steradians, std::ratio<1>>)
UNIT_ADD_CATEGORY_TRAIT(solid_angle)
#endif
//------------------------------
// FREQUENCY UNITS
//------------------------------
/**
* @namespace units::frequency
* @brief namespace for unit types and containers representing frequency values
* @details The SI unit for frequency is `hertz`, and the corresponding `base_unit` category is
* `frequency_unit`.
* @anchor frequencyContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_FREQUENCY_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(frequency, hertz, hertz, Hz, unit<std::ratio<1>, units::category::frequency_unit>)
UNIT_ADD_CATEGORY_TRAIT(frequency)
#endif
//------------------------------
// VELOCITY UNITS
//------------------------------
/**
* @namespace units::velocity
* @brief namespace for unit types and containers representing velocity values
* @details The SI unit for velocity is `meters_per_second`, and the corresponding `base_unit` category is
* `velocity_unit`.
* @anchor velocityContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_VELOCITY_UNITS)
UNIT_ADD(velocity, meters_per_second, meters_per_second, mps, unit<std::ratio<1>, units::category::velocity_unit>)
UNIT_ADD(velocity, feet_per_second, feet_per_second, fps, compound_unit<length::feet, inverse<time::seconds>>)
UNIT_ADD(velocity, miles_per_hour, miles_per_hour, mph, compound_unit<length::miles, inverse<time::hour>>)
UNIT_ADD(velocity, kilometers_per_hour, kilometers_per_hour, kph, compound_unit<length::kilometers, inverse<time::hour>>)
UNIT_ADD(velocity, knot, knots, kts, compound_unit<length::nauticalMiles, inverse<time::hour>>)
UNIT_ADD_CATEGORY_TRAIT(velocity)
#endif
//------------------------------
// ANGULAR VELOCITY UNITS
//------------------------------
/**
* @namespace units::angular_velocity
* @brief namespace for unit types and containers representing angular velocity values
* @details The SI unit for angular velocity is `radians_per_second`, and the corresponding `base_unit` category is
* `angular_velocity_unit`.
* @anchor angularVelocityContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGULAR_VELOCITY_UNITS)
UNIT_ADD(angular_velocity, radians_per_second, radians_per_second, rad_per_s, unit<std::ratio<1>, units::category::angular_velocity_unit>)
UNIT_ADD(angular_velocity, degrees_per_second, degrees_per_second, deg_per_s, compound_unit<angle::degrees, inverse<time::seconds>>)
UNIT_ADD(angular_velocity, revolutions_per_minute, revolutions_per_minute, rpm, unit<std::ratio<2, 60>, radians_per_second, std::ratio<1>>)
UNIT_ADD(angular_velocity, milliarcseconds_per_year, milliarcseconds_per_year, mas_per_yr, compound_unit<angle::milliarcseconds, inverse<time::year>>)
UNIT_ADD_CATEGORY_TRAIT(angular_velocity)
#endif
//------------------------------
// UNITS OF ACCELERATION
//------------------------------
/**
* @namespace units::acceleration
* @brief namespace for unit types and containers representing acceleration values
* @details The SI unit for acceleration is `meters_per_second_squared`, and the corresponding `base_unit` category is
* `acceleration_unit`.
* @anchor accelerationContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ACCELERATION_UNITS)
UNIT_ADD(acceleration, meters_per_second_squared, meters_per_second_squared, mps_sq, unit<std::ratio<1>, units::category::acceleration_unit>)
UNIT_ADD(acceleration, feet_per_second_squared, feet_per_second_squared, fps_sq, compound_unit<length::feet, inverse<squared<time::seconds>>>)
UNIT_ADD(acceleration, standard_gravity, standard_gravity, SG, unit<std::ratio<980665, 100000>, meters_per_second_squared>)
UNIT_ADD_CATEGORY_TRAIT(acceleration)
#endif
//------------------------------
// UNITS OF FORCE
//------------------------------
/**
* @namespace units::force
* @brief namespace for unit types and containers representing force values
* @details The SI unit for force is `newtons`, and the corresponding `base_unit` category is
* `force_unit`.
* @anchor forceContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_FORCE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(force, newton, newtons, N, unit<std::ratio<1>, units::category::force_unit>)
UNIT_ADD(force, pound, pounds, lbf, compound_unit<mass::slug, length::foot, inverse<squared<time::seconds>>>)
UNIT_ADD(force, dyne, dynes, dyn, unit<std::ratio<1, 100000>, newtons>)
UNIT_ADD(force, kilopond, kiloponds, kp, compound_unit<acceleration::standard_gravity, mass::kilograms>)
UNIT_ADD(force, poundal, poundals, pdl, compound_unit<mass::pound, length::foot, inverse<squared<time::seconds>>>)
UNIT_ADD_CATEGORY_TRAIT(force)
#endif
//------------------------------
// UNITS OF PRESSURE
//------------------------------
/**
* @namespace units::pressure
* @brief namespace for unit types and containers representing pressure values
* @details The SI unit for pressure is `pascals`, and the corresponding `base_unit` category is
* `pressure_unit`.
* @anchor pressureContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_PRESSURE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(pressure, pascal, pascals, Pa, unit<std::ratio<1>, units::category::pressure_unit>)
UNIT_ADD(pressure, bar, bars, bar, unit<std::ratio<100>, kilo<pascals>>)
UNIT_ADD(pressure, mbar, mbars, mbar, unit<std::ratio<1>, milli<bar>>)
UNIT_ADD(pressure, atmosphere, atmospheres, atm, unit<std::ratio<101325>, pascals>)
UNIT_ADD(pressure, pounds_per_square_inch, pounds_per_square_inch, psi, compound_unit<force::pounds, inverse<squared<length::inch>>>)
UNIT_ADD(pressure, torr, torrs, torr, unit<std::ratio<1, 760>, atmospheres>)
UNIT_ADD_CATEGORY_TRAIT(pressure)
#endif
//------------------------------
// UNITS OF CHARGE
//------------------------------
/**
* @namespace units::charge
* @brief namespace for unit types and containers representing charge values
* @details The SI unit for charge is `coulombs`, and the corresponding `base_unit` category is
* `charge_unit`.
* @anchor chargeContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_CHARGE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(charge, coulomb, coulombs, C, unit<std::ratio<1>, units::category::charge_unit>)
UNIT_ADD_WITH_METRIC_PREFIXES(charge, ampere_hour, ampere_hours, Ah, compound_unit<current::ampere, time::hours>)
UNIT_ADD_CATEGORY_TRAIT(charge)
#endif
//------------------------------
// UNITS OF ENERGY
//------------------------------
/**
* @namespace units::energy
* @brief namespace for unit types and containers representing energy values
* @details The SI unit for energy is `joules`, and the corresponding `base_unit` category is
* `energy_unit`.
* @anchor energyContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ENERGY_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(energy, joule, joules, J, unit<std::ratio<1>, units::category::energy_unit>)
UNIT_ADD_WITH_METRIC_PREFIXES(energy, calorie, calories, cal, unit<std::ratio<4184, 1000>, joules>)
UNIT_ADD(energy, kilowatt_hour, kilowatt_hours, kWh, unit<std::ratio<36, 10>, megajoules>)
UNIT_ADD(energy, watt_hour, watt_hours, Wh, unit<std::ratio<1, 1000>, kilowatt_hours>)
UNIT_ADD(energy, british_thermal_unit, british_thermal_units, BTU, unit<std::ratio<105505585262, 100000000>, joules>)
UNIT_ADD(energy, british_thermal_unit_iso, british_thermal_units_iso, BTU_iso, unit<std::ratio<1055056, 1000>, joules>)
UNIT_ADD(energy, british_thermal_unit_59, british_thermal_units_59, BTU59, unit<std::ratio<1054804, 1000>, joules>)
UNIT_ADD(energy, therm, therms, thm, unit<std::ratio<100000>, british_thermal_units_59>)
UNIT_ADD(energy, foot_pound, foot_pounds, ftlbf, unit<std::ratio<13558179483314004, 10000000000000000>, joules>)
UNIT_ADD_CATEGORY_TRAIT(energy)
#endif
//------------------------------
// UNITS OF POWER
//------------------------------
/**
* @namespace units::power
* @brief namespace for unit types and containers representing power values
* @details The SI unit for power is `watts`, and the corresponding `base_unit` category is
* `power_unit`.
* @anchor powerContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_POWER_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(power, watt, watts, W, unit<std::ratio<1>, units::category::power_unit>)
UNIT_ADD(power, horsepower, horsepower, hp, unit<std::ratio<7457, 10>, watts>)
UNIT_ADD_DECIBEL(power, watt, dBW)
UNIT_ADD_DECIBEL(power, milliwatt, dBm)
UNIT_ADD_CATEGORY_TRAIT(power)
#endif
//------------------------------
// UNITS OF VOLTAGE
//------------------------------
/**
* @namespace units::voltage
* @brief namespace for unit types and containers representing voltage values
* @details The SI unit for voltage is `volts`, and the corresponding `base_unit` category is
* `voltage_unit`.
* @anchor voltageContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_VOLTAGE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(voltage, volt, volts, V, unit<std::ratio<1>, units::category::voltage_unit>)
UNIT_ADD(voltage, statvolt, statvolts, statV, unit<std::ratio<1000000, 299792458>, volts>)
UNIT_ADD(voltage, abvolt, abvolts, abV, unit<std::ratio<1, 100000000>, volts>)
UNIT_ADD_CATEGORY_TRAIT(voltage)
#endif
//------------------------------
// UNITS OF CAPACITANCE
//------------------------------
/**
* @namespace units::capacitance
* @brief namespace for unit types and containers representing capacitance values
* @details The SI unit for capacitance is `farads`, and the corresponding `base_unit` category is
* `capacitance_unit`.
* @anchor capacitanceContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_CAPACITANCE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(capacitance, farad, farads, F, unit<std::ratio<1>, units::category::capacitance_unit>)
UNIT_ADD_CATEGORY_TRAIT(capacitance)
#endif
//------------------------------
// UNITS OF IMPEDANCE
//------------------------------
/**
* @namespace units::impedance
* @brief namespace for unit types and containers representing impedance values
* @details The SI unit for impedance is `ohms`, and the corresponding `base_unit` category is
* `impedance_unit`.
* @anchor impedanceContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_IMPEDANCE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(impedance, ohm, ohms, Ohm, unit<std::ratio<1>, units::category::impedance_unit>)
UNIT_ADD_CATEGORY_TRAIT(impedance)
#endif
//------------------------------
// UNITS OF CONDUCTANCE
//------------------------------
/**
* @namespace units::conductance
* @brief namespace for unit types and containers representing conductance values
* @details The SI unit for conductance is `siemens`, and the corresponding `base_unit` category is
* `conductance_unit`.
* @anchor conductanceContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_CONDUCTANCE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(conductance, siemens, siemens, S, unit<std::ratio<1>, units::category::conductance_unit>)
UNIT_ADD_CATEGORY_TRAIT(conductance)
#endif
//------------------------------
// UNITS OF MAGNETIC FLUX
//------------------------------
/**
* @namespace units::magnetic_flux
* @brief namespace for unit types and containers representing magnetic_flux values
* @details The SI unit for magnetic_flux is `webers`, and the corresponding `base_unit` category is
* `magnetic_flux_unit`.
* @anchor magneticFluxContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_MAGNETIC_FLUX_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(magnetic_flux, weber, webers, Wb, unit<std::ratio<1>, units::category::magnetic_flux_unit>)
UNIT_ADD(magnetic_flux, maxwell, maxwells, Mx, unit<std::ratio<1, 100000000>, webers>)
UNIT_ADD_CATEGORY_TRAIT(magnetic_flux)
#endif
//----------------------------------------
// UNITS OF MAGNETIC FIELD STRENGTH
//----------------------------------------
/**
* @namespace units::magnetic_field_strength
* @brief namespace for unit types and containers representing magnetic_field_strength values
* @details The SI unit for magnetic_field_strength is `teslas`, and the corresponding `base_unit` category is
* `magnetic_field_strength_unit`.
* @anchor magneticFieldStrengthContainers
* @sa See unit_t for more information on unit type containers.
*/
// Unfortunately `_T` is a WINAPI macro, so we have to use `_Te` as the tesla abbreviation.
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_MAGNETIC_FIELD_STRENGTH_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(magnetic_field_strength, tesla, teslas, Te, unit<std::ratio<1>, units::category::magnetic_field_strength_unit>)
UNIT_ADD(magnetic_field_strength, gauss, gauss, G, compound_unit<magnetic_flux::maxwell, inverse<squared<length::centimeter>>>)
UNIT_ADD_CATEGORY_TRAIT(magnetic_field_strength)
#endif
//------------------------------
// UNITS OF INDUCTANCE
//------------------------------
/**
* @namespace units::inductance
* @brief namespace for unit types and containers representing inductance values
* @details The SI unit for inductance is `henrys`, and the corresponding `base_unit` category is
* `inductance_unit`.
* @anchor inductanceContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_INDUCTANCE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(inductance, henry, henries, H, unit<std::ratio<1>, units::category::inductance_unit>)
UNIT_ADD_CATEGORY_TRAIT(inductance)
#endif
//------------------------------
// UNITS OF LUMINOUS FLUX
//------------------------------
/**
* @namespace units::luminous_flux
* @brief namespace for unit types and containers representing luminous_flux values
* @details The SI unit for luminous_flux is `lumens`, and the corresponding `base_unit` category is
* `luminous_flux_unit`.
* @anchor luminousFluxContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_LUMINOUS_FLUX_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(luminous_flux, lumen, lumens, lm, unit<std::ratio<1>, units::category::luminous_flux_unit>)
UNIT_ADD_CATEGORY_TRAIT(luminous_flux)
#endif
//------------------------------
// UNITS OF ILLUMINANCE
//------------------------------
/**
* @namespace units::illuminance
* @brief namespace for unit types and containers representing illuminance values
* @details The SI unit for illuminance is `luxes`, and the corresponding `base_unit` category is
* `illuminance_unit`.
* @anchor illuminanceContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ILLUMINANCE_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(illuminance, lux, luxes, lx, unit<std::ratio<1>, units::category::illuminance_unit>)
UNIT_ADD(illuminance, footcandle, footcandles, fc, compound_unit<luminous_flux::lumen, inverse<squared<length::foot>>>)
UNIT_ADD(illuminance, lumens_per_square_inch, lumens_per_square_inch, lm_per_in_sq, compound_unit<luminous_flux::lumen, inverse<squared<length::inch>>>)
UNIT_ADD(illuminance, phot, phots, ph, compound_unit<luminous_flux::lumens, inverse<squared<length::centimeter>>>)
UNIT_ADD_CATEGORY_TRAIT(illuminance)
#endif
//------------------------------
// UNITS OF RADIATION
//------------------------------
/**
* @namespace units::radiation
* @brief namespace for unit types and containers representing radiation values
* @details The SI units for radiation are:
* - source activity: becquerel
* - absorbed dose: gray
* - equivalent dose: sievert
* @anchor radiationContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_RADIATION_UNITS)
UNIT_ADD_WITH_METRIC_PREFIXES(radiation, becquerel, becquerels, Bq, unit<std::ratio<1>, units::frequency::hertz>)
UNIT_ADD_WITH_METRIC_PREFIXES(radiation, gray, grays, Gy, compound_unit<energy::joules, inverse<mass::kilogram>>)
UNIT_ADD_WITH_METRIC_PREFIXES(radiation, sievert, sieverts, Sv, unit<std::ratio<1>, grays>)
UNIT_ADD(radiation, curie, curies, Ci, unit<std::ratio<37>, gigabecquerels>)
UNIT_ADD(radiation, rutherford, rutherfords, rd, unit<std::ratio<1>, megabecquerels>)
UNIT_ADD(radiation, rad, rads, rads, unit<std::ratio<1>, centigrays>)
UNIT_ADD_CATEGORY_TRAIT(radioactivity)
#endif
//------------------------------
// UNITS OF TORQUE
//------------------------------
/**
* @namespace units::torque
* @brief namespace for unit types and containers representing torque values
* @details The SI unit for torque is `newton_meters`, and the corresponding `base_unit` category is
* `torque_units`.
* @anchor torqueContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_TORQUE_UNITS)
UNIT_ADD(torque, newton_meter, newton_meters, Nm, unit<std::ratio<1>, units::energy::joule>)
UNIT_ADD(torque, foot_pound, foot_pounds, ftlb, compound_unit<length::foot, force::pounds>)
UNIT_ADD(torque, foot_poundal, foot_poundals, ftpdl, compound_unit<length::foot, force::poundal>)
UNIT_ADD(torque, inch_pound, inch_pounds, inlb, compound_unit<length::inch, force::pounds>)
UNIT_ADD(torque, meter_kilogram, meter_kilograms, mkgf, compound_unit<length::meter, force::kiloponds>)
UNIT_ADD_CATEGORY_TRAIT(torque)
#endif
//------------------------------
// AREA UNITS
//------------------------------
/**
* @namespace units::area
* @brief namespace for unit types and containers representing area values
* @details The SI unit for area is `square_meters`, and the corresponding `base_unit` category is
* `area_unit`.
* @anchor areaContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_AREA_UNITS)
UNIT_ADD(area, square_meter, square_meters, sq_m, unit<std::ratio<1>, units::category::area_unit>)
UNIT_ADD(area, square_foot, square_feet, sq_ft, squared<length::feet>)
UNIT_ADD(area, square_inch, square_inches, sq_in, squared<length::inch>)
UNIT_ADD(area, square_mile, square_miles, sq_mi, squared<length::miles>)
UNIT_ADD(area, square_kilometer, square_kilometers, sq_km, squared<length::kilometers>)
UNIT_ADD(area, hectare, hectares, ha, unit<std::ratio<10000>, square_meters>)
UNIT_ADD(area, acre, acres, acre, unit<std::ratio<43560>, square_feet>)
UNIT_ADD_CATEGORY_TRAIT(area)
#endif
//------------------------------
// UNITS OF VOLUME
//------------------------------
/**
* @namespace units::volume
* @brief namespace for unit types and containers representing volume values
* @details The SI unit for volume is `cubic_meters`, and the corresponding `base_unit` category is
* `volume_unit`.
* @anchor volumeContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_VOLUME_UNITS)
UNIT_ADD(volume, cubic_meter, cubic_meters, cu_m, unit<std::ratio<1>, units::category::volume_unit>)
UNIT_ADD(volume, cubic_millimeter, cubic_millimeters, cu_mm, cubed<length::millimeter>)
UNIT_ADD(volume, cubic_kilometer, cubic_kilometers, cu_km, cubed<length::kilometer>)
UNIT_ADD_WITH_METRIC_PREFIXES(volume, liter, liters, L, cubed<deci<length::meter>>)
UNIT_ADD(volume, cubic_inch, cubic_inches, cu_in, cubed<length::inches>)
UNIT_ADD(volume, cubic_foot, cubic_feet, cu_ft, cubed<length::feet>)
UNIT_ADD(volume, cubic_yard, cubic_yards, cu_yd, cubed<length::yards>)
UNIT_ADD(volume, cubic_mile, cubic_miles, cu_mi, cubed<length::miles>)
UNIT_ADD(volume, gallon, gallons, gal, unit<std::ratio<231>, cubic_inches>)
UNIT_ADD(volume, quart, quarts, qt, unit<std::ratio<1, 4>, gallons>)
UNIT_ADD(volume, pint, pints, pt, unit<std::ratio<1, 2>, quarts>)
UNIT_ADD(volume, cup, cups, c, unit<std::ratio<1, 2>, pints>)
UNIT_ADD(volume, fluid_ounce, fluid_ounces, fl_oz, unit<std::ratio<1, 8>, cups>)
UNIT_ADD(volume, barrel, barrels, bl, unit<std::ratio<42>, gallons>)
UNIT_ADD(volume, bushel, bushels, bu, unit<std::ratio<215042, 100>, cubic_inches>)
UNIT_ADD(volume, cord, cords, cord, unit<std::ratio<128>, cubic_feet>)
UNIT_ADD(volume, cubic_fathom, cubic_fathoms, cu_fm, cubed<length::fathom>)
UNIT_ADD(volume, tablespoon, tablespoons, tbsp, unit<std::ratio<1, 2>, fluid_ounces>)
UNIT_ADD(volume, teaspoon, teaspoons, tsp, unit<std::ratio<1, 6>, fluid_ounces>)
UNIT_ADD(volume, pinch, pinches, pinch, unit<std::ratio<1, 8>, teaspoons>)
UNIT_ADD(volume, dash, dashes, dash, unit<std::ratio<1, 2>, pinches>)
UNIT_ADD(volume, drop, drops, drop, unit<std::ratio<1, 360>, fluid_ounces>)
UNIT_ADD(volume, fifth, fifths, fifth, unit<std::ratio<1, 5>, gallons>)
UNIT_ADD(volume, dram, drams, dr, unit<std::ratio<1, 8>, fluid_ounces>)
UNIT_ADD(volume, gill, gills, gi, unit<std::ratio<4>, fluid_ounces>)
UNIT_ADD(volume, peck, pecks, pk, unit<std::ratio<1, 4>, bushels>)
UNIT_ADD(volume, sack, sacks, sacks, unit<std::ratio<3>, bushels>)
UNIT_ADD(volume, shot, shots, shots, unit<std::ratio<3, 2>, fluid_ounces>)
UNIT_ADD(volume, strike, strikes, strikes, unit<std::ratio<2>, bushels>)
UNIT_ADD_CATEGORY_TRAIT(volume)
#endif
//------------------------------
// UNITS OF DENSITY
//------------------------------
/**
* @namespace units::density
* @brief namespace for unit types and containers representing density values
* @details The SI unit for density is `kilograms_per_cubic_meter`, and the corresponding `base_unit` category is
* `density_unit`.
* @anchor densityContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_DENSITY_UNITS)
UNIT_ADD(density, kilograms_per_cubic_meter, kilograms_per_cubic_meter, kg_per_cu_m, unit<std::ratio<1>, units::category::density_unit>)
UNIT_ADD(density, grams_per_milliliter, grams_per_milliliter, g_per_mL, compound_unit<mass::grams, inverse<volume::milliliter>>)
UNIT_ADD(density, kilograms_per_liter, kilograms_per_liter, kg_per_L, unit<std::ratio<1>, compound_unit<mass::grams, inverse<volume::milliliter>>>)
UNIT_ADD(density, ounces_per_cubic_foot, ounces_per_cubic_foot, oz_per_cu_ft, compound_unit<mass::ounces, inverse<volume::cubic_foot>>)
UNIT_ADD(density, ounces_per_cubic_inch, ounces_per_cubic_inch, oz_per_cu_in, compound_unit<mass::ounces, inverse<volume::cubic_inch>>)
UNIT_ADD(density, ounces_per_gallon, ounces_per_gallon, oz_per_gal, compound_unit<mass::ounces, inverse<volume::gallon>>)
UNIT_ADD(density, pounds_per_cubic_foot, pounds_per_cubic_foot, lb_per_cu_ft, compound_unit<mass::pounds, inverse<volume::cubic_foot>>)
UNIT_ADD(density, pounds_per_cubic_inch, pounds_per_cubic_inch, lb_per_cu_in, compound_unit<mass::pounds, inverse<volume::cubic_inch>>)
UNIT_ADD(density, pounds_per_gallon, pounds_per_gallon, lb_per_gal, compound_unit<mass::pounds, inverse<volume::gallon>>)
UNIT_ADD(density, slugs_per_cubic_foot, slugs_per_cubic_foot, slug_per_cu_ft, compound_unit<mass::slugs, inverse<volume::cubic_foot>>)
UNIT_ADD_CATEGORY_TRAIT(density)
#endif
//------------------------------
// UNITS OF CONCENTRATION
//------------------------------
/**
* @namespace units::concentration
* @brief namespace for unit types and containers representing concentration values
* @details The SI unit for concentration is `parts_per_million`, and the corresponding `base_unit` category is
* `scalar_unit`.
* @anchor concentrationContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_CONCENTRATION_UNITS)
UNIT_ADD(concentration, ppm, parts_per_million, ppm, unit<std::ratio<1, 1000000>, units::category::scalar_unit>)
UNIT_ADD(concentration, ppb, parts_per_billion, ppb, unit<std::ratio<1, 1000>, parts_per_million>)
UNIT_ADD(concentration, ppt, parts_per_trillion, ppt, unit<std::ratio<1, 1000>, parts_per_billion>)
UNIT_ADD(concentration, percent, percent, pct, unit<std::ratio<1, 100>, units::category::scalar_unit>)
UNIT_ADD_CATEGORY_TRAIT(concentration)
#endif
//------------------------------
// UNITS OF DATA
//------------------------------
/**
* @namespace units::data
* @brief namespace for unit types and containers representing data values
* @details The base unit for data is `bytes`, and the corresponding `base_unit` category is
* `data_unit`.
* @anchor dataContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_DATA_UNITS)
UNIT_ADD_WITH_METRIC_AND_BINARY_PREFIXES(data, byte, bytes, B, unit<std::ratio<1>, units::category::data_unit>)
UNIT_ADD(data, exabyte, exabytes, EB, unit<std::ratio<1000>, petabytes>)
UNIT_ADD_WITH_METRIC_AND_BINARY_PREFIXES(data, bit, bits, b, unit<std::ratio<1, 8>, byte>)
UNIT_ADD(data, exabit, exabits, Eb, unit<std::ratio<1000>, petabits>)
UNIT_ADD_CATEGORY_TRAIT(data)
#endif
//------------------------------
// UNITS OF DATA TRANSFER
//------------------------------
/**
* @namespace units::data_transfer_rate
* @brief namespace for unit types and containers representing data values
* @details The base unit for data is `bytes`, and the corresponding `base_unit` category is
* `data_unit`.
* @anchor dataContainers
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_DATA_TRANSFER_RATE_UNITS)
UNIT_ADD_WITH_METRIC_AND_BINARY_PREFIXES(data_transfer_rate, bytes_per_second, bytes_per_second, Bps, unit<std::ratio<1>, units::category::data_transfer_rate_unit>)
UNIT_ADD(data_transfer_rate, exabytes_per_second, exabytes_per_second, EBps, unit<std::ratio<1000>, petabytes_per_second>)
UNIT_ADD_WITH_METRIC_AND_BINARY_PREFIXES(data_transfer_rate, bits_per_second, bits_per_second, bps, unit<std::ratio<1, 8>, bytes_per_second>)
UNIT_ADD(data_transfer_rate, exabits_per_second, exabits_per_second, Ebps, unit<std::ratio<1000>, petabits_per_second>)
UNIT_ADD_CATEGORY_TRAIT(data_transfer_rate)
#endif
//------------------------------
// CONSTANTS
//------------------------------
/**
* @brief namespace for physical constants like PI and Avogadro's Number.
* @sa See unit_t for more information on unit type containers.
*/
#if !defined(DISABLE_PREDEFINED_UNITS)
namespace constants
{
/**
* @name Unit Containers
* @anchor constantContainers
* @{
*/
using PI = unit<std::ratio<1>, dimensionless::scalar, std::ratio<1>>;
static constexpr const unit_t<PI> pi(1); ///< Ratio of a circle's circumference to its diameter.
static constexpr const velocity::meters_per_second_t c(299792458.0); ///< Speed of light in vacuum.
static constexpr const unit_t<compound_unit<cubed<length::meters>, inverse<mass::kilogram>, inverse<squared<time::seconds>>>> G(6.67408e-11); ///< Newtonian constant of gravitation.
static constexpr const unit_t<compound_unit<energy::joule, time::seconds>> h(6.626070040e-34); ///< Planck constant.
static constexpr const unit_t<compound_unit<force::newtons, inverse<squared<current::ampere>>>> mu0(pi * 4.0e-7 * force::newton_t(1) / units::math::cpow<2>(current::ampere_t(1))); ///< vacuum permeability.
static constexpr const unit_t<compound_unit<capacitance::farad, inverse<length::meter>>> epsilon0(1.0 / (mu0 * math::cpow<2>(c))); ///< vacuum permitivity.
static constexpr const impedance::ohm_t Z0(mu0 * c); ///< characteristic impedance of vacuum.
static constexpr const unit_t<compound_unit<force::newtons, area::square_meter, inverse<squared<charge::coulomb>>>> k_e(1.0 / (4 * pi * epsilon0)); ///< Coulomb's constant.
static constexpr const charge::coulomb_t e(1.6021766208e-19); ///< elementary charge.
static constexpr const mass::kilogram_t m_e(9.10938356e-31); ///< electron mass.
static constexpr const mass::kilogram_t m_p(1.672621898e-27); ///< proton mass.
static constexpr const unit_t<compound_unit<energy::joules, inverse<magnetic_field_strength::tesla>>> mu_B(e * h / (4 * pi *m_e)); ///< Bohr magneton.
static constexpr const unit_t<inverse<substance::mol>> N_A(6.022140857e23); ///< Avagadro's Number.
static constexpr const unit_t<compound_unit<energy::joules, inverse<temperature::kelvin>, inverse<substance::moles>>> R(8.3144598); ///< Gas constant.
static constexpr const unit_t<compound_unit<energy::joules, inverse<temperature::kelvin>>> k_B(R / N_A); ///< Boltzmann constant.
static constexpr const unit_t<compound_unit<charge::coulomb, inverse<substance::mol>>> F(N_A * e); ///< Faraday constant.
static constexpr const unit_t<compound_unit<power::watts, inverse<area::square_meters>, inverse<squared<squared<temperature::kelvin>>>>> sigma((2 * math::cpow<5>(pi) * math::cpow<4>(R)) / (15 * math::cpow<3>(h) * math::cpow<2>(c) * math::cpow<4>(N_A))); ///< Stefan-Boltzmann constant.
/** @} */
}
#endif
//----------------------------------
// UNIT-ENABLED CMATH FUNCTIONS
//----------------------------------
/**
* @brief namespace for unit-enabled versions of the `<cmath>` library
* @details Includes trigonometric functions, exponential/log functions, rounding functions, etc.
* @sa See `unit_t` for more information on unit type containers.
*/
namespace math
{
//----------------------------------
// MIN/MAX FUNCTIONS
//----------------------------------
template<class UnitTypeLhs, class UnitTypeRhs>
UnitTypeLhs min(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs)
{
static_assert(traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value, "Unit types are not compatible.");
UnitTypeLhs r(rhs);
return (lhs < r ? lhs : r);
}
template<class UnitTypeLhs, class UnitTypeRhs>
UnitTypeLhs max(const UnitTypeLhs& lhs, const UnitTypeRhs& rhs)
{
static_assert(traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value, "Unit types are not compatible.");
UnitTypeLhs r(rhs);
return (lhs > r ? lhs : r);
}
//----------------------------------
// TRIGONOMETRIC FUNCTIONS
//----------------------------------
/**
* @ingroup UnitMath
* @brief Compute cosine
* @details The input value can be in any unit of angle, including radians or degrees.
* @tparam AngleUnit any `unit_t` type of `category::angle_unit`.
* @param[in] angle angle to compute the cosine of
* @returns Returns the cosine of <i>angle</i>
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class AngleUnit>
dimensionless::scalar_t cos(const AngleUnit angle) noexcept
{
static_assert(traits::is_angle_unit<AngleUnit>::value, "Type `AngleUnit` must be a unit of angle derived from `unit_t`.");
return dimensionless::scalar_t(std::cos(angle.template convert<angle::radian>()()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute sine
* @details The input value can be in any unit of angle, including radians or degrees.
* @tparam AngleUnit any `unit_t` type of `category::angle_unit`.
* @param[in] angle angle to compute the since of
* @returns Returns the sine of <i>angle</i>
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class AngleUnit>
dimensionless::scalar_t sin(const AngleUnit angle) noexcept
{
static_assert(traits::is_angle_unit<AngleUnit>::value, "Type `AngleUnit` must be a unit of angle derived from `unit_t`.");
return dimensionless::scalar_t(std::sin(angle.template convert<angle::radian>()()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute tangent
* @details The input value can be in any unit of angle, including radians or degrees.
* @tparam AngleUnit any `unit_t` type of `category::angle_unit`.
* @param[in] angle angle to compute the tangent of
* @returns Returns the tangent of <i>angle</i>
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class AngleUnit>
dimensionless::scalar_t tan(const AngleUnit angle) noexcept
{
static_assert(traits::is_angle_unit<AngleUnit>::value, "Type `AngleUnit` must be a unit of angle derived from `unit_t`.");
return dimensionless::scalar_t(std::tan(angle.template convert<angle::radian>()()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute arc cosine
* @details Returns the principal value of the arc cosine of x, expressed in radians.
* @param[in] x Value whose arc cosine is computed, in the interval [-1,+1].
* @returns Principal arc cosine of x, in the interval [0,pi] radians.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class ScalarUnit>
angle::radian_t acos(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return angle::radian_t(std::acos(x()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute arc sine
* @details Returns the principal value of the arc sine of x, expressed in radians.
* @param[in] x Value whose arc sine is computed, in the interval [-1,+1].
* @returns Principal arc sine of x, in the interval [-pi/2,+pi/2] radians.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class ScalarUnit>
angle::radian_t asin(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return angle::radian_t(std::asin(x()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute arc tangent
* @details Returns the principal value of the arc tangent of x, expressed in radians.
* Notice that because of the sign ambiguity, the function cannot determine with
* certainty in which quadrant the angle falls only by its tangent value. See
* atan2 for an alternative that takes a fractional argument instead.
* @tparam AngleUnit any `unit_t` type of `category::angle_unit`.
* @param[in] x Value whose arc tangent is computed, in the interval [-1,+1].
* @returns Principal arc tangent of x, in the interval [-pi/2,+pi/2] radians.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class ScalarUnit>
angle::radian_t atan(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return angle::radian_t(std::atan(x()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute arc tangent with two parameters
* @details To compute the value, the function takes into account the sign of both arguments in order to determine the quadrant.
* @param[in] y y-component of the triangle expressed.
* @param[in] x x-component of the triangle expressed.
* @returns Returns the principal value of the arc tangent of <i>y/x</i>, expressed in radians.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class Y, class X>
angle::radian_t atan2(const Y y, const X x) noexcept
{
static_assert(traits::is_dimensionless_unit<decltype(y/x)>::value, "The quantity y/x must yield a dimensionless ratio.");
// X and Y could be different length units, so normalize them
return angle::radian_t(std::atan2(y.template convert<typename units::traits::unit_t_traits<X>::unit_type>()(), x()));
}
#endif
//----------------------------------
// HYPERBOLIC TRIG FUNCTIONS
//----------------------------------
/**
* @ingroup UnitMath
* @brief Compute hyperbolic cosine
* @details The input value can be in any unit of angle, including radians or degrees.
* @tparam AngleUnit any `unit_t` type of `category::angle_unit`.
* @param[in] angle angle to compute the hyperbolic cosine of
* @returns Returns the hyperbolic cosine of <i>angle</i>
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class AngleUnit>
dimensionless::scalar_t cosh(const AngleUnit angle) noexcept
{
static_assert(traits::is_angle_unit<AngleUnit>::value, "Type `AngleUnit` must be a unit of angle derived from `unit_t`.");
return dimensionless::scalar_t(std::cosh(angle.template convert<angle::radian>()()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute hyperbolic sine
* @details The input value can be in any unit of angle, including radians or degrees.
* @tparam AngleUnit any `unit_t` type of `category::angle_unit`.
* @param[in] angle angle to compute the hyperbolic sine of
* @returns Returns the hyperbolic sine of <i>angle</i>
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class AngleUnit>
dimensionless::scalar_t sinh(const AngleUnit angle) noexcept
{
static_assert(traits::is_angle_unit<AngleUnit>::value, "Type `AngleUnit` must be a unit of angle derived from `unit_t`.");
return dimensionless::scalar_t(std::sinh(angle.template convert<angle::radian>()()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute hyperbolic tangent
* @details The input value can be in any unit of angle, including radians or degrees.
* @tparam AngleUnit any `unit_t` type of `category::angle_unit`.
* @param[in] angle angle to compute the hyperbolic tangent of
* @returns Returns the hyperbolic tangent of <i>angle</i>
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class AngleUnit>
dimensionless::scalar_t tanh(const AngleUnit angle) noexcept
{
static_assert(traits::is_angle_unit<AngleUnit>::value, "Type `AngleUnit` must be a unit of angle derived from `unit_t`.");
return dimensionless::scalar_t(std::tanh(angle.template convert<angle::radian>()()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute arc hyperbolic cosine
* @details Returns the nonnegative arc hyperbolic cosine of x, expressed in radians.
* @param[in] x Value whose arc hyperbolic cosine is computed. If the argument is less
* than 1, a domain error occurs.
* @returns Nonnegative arc hyperbolic cosine of x, in the interval [0,+INFINITY] radians.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class ScalarUnit>
angle::radian_t acosh(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return angle::radian_t(std::acosh(x()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute arc hyperbolic sine
* @details Returns the arc hyperbolic sine of x, expressed in radians.
* @param[in] x Value whose arc hyperbolic sine is computed.
* @returns Arc hyperbolic sine of x, in radians.
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class ScalarUnit>
angle::radian_t asinh(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return angle::radian_t(std::asinh(x()));
}
#endif
/**
* @ingroup UnitMath
* @brief Compute arc hyperbolic tangent
* @details Returns the arc hyperbolic tangent of x, expressed in radians.
* @param[in] x Value whose arc hyperbolic tangent is computed, in the interval [-1,+1].
* If the argument is out of this interval, a domain error occurs. For
* values of -1 and +1, a pole error may occur.
* @returns units::angle::radian_t
*/
#if !defined(DISABLE_PREDEFINED_UNITS) || defined(ENABLE_PREDEFINED_ANGLE_UNITS)
template<class ScalarUnit>
angle::radian_t atanh(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return angle::radian_t(std::atanh(x()));
}
#endif
//----------------------------------
// TRANSCENDENTAL FUNCTIONS
//----------------------------------
// it makes NO SENSE to put dimensioned units into a transcendental function, and if you think it does you are
// demonstrably wrong. https://en.wikipedia.org/wiki/Transcendental_function#Dimensional_analysis
/**
* @ingroup UnitMath
* @brief Compute exponential function
* @details Returns the base-e exponential function of x, which is e raised to the power x: ex.
* @param[in] x scalar value of the exponent.
* @returns Exponential value of x.
* If the magnitude of the result is too large to be represented by a value of the return type, the
* function returns HUGE_VAL (or HUGE_VALF or HUGE_VALL) with the proper sign, and an overflow range error occurs
*/
template<class ScalarUnit>
dimensionless::scalar_t exp(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return dimensionless::scalar_t(std::exp(x()));
}
/**
* @ingroup UnitMath
* @brief Compute natural logarithm
* @details Returns the natural logarithm of x.
* @param[in] x scalar value whose logarithm is calculated. If the argument is negative, a
* domain error occurs.
* @sa log10 for more common base-10 logarithms
* @returns Natural logarithm of x.
*/
template<class ScalarUnit>
dimensionless::scalar_t log(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return dimensionless::scalar_t(std::log(x()));
}
/**
* @ingroup UnitMath
* @brief Compute common logarithm
* @details Returns the common (base-10) logarithm of x.
* @param[in] x Value whose logarithm is calculated. If the argument is negative, a
* domain error occurs.
* @returns Common logarithm of x.
*/
template<class ScalarUnit>
dimensionless::scalar_t log10(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return dimensionless::scalar_t(std::log10(x()));
}
/**
* @ingroup UnitMath
* @brief Break into fractional and integral parts.
* @details The integer part is stored in the object pointed by intpart, and the
* fractional part is returned by the function. Both parts have the same sign
* as x.
* @param[in] x scalar value to break into parts.
* @param[in] intpart Pointer to an object (of the same type as x) where the integral part
* is stored with the same sign as x.
* @returns The fractional part of x, with the same sign.
*/
template<class ScalarUnit>
dimensionless::scalar_t modf(const ScalarUnit x, ScalarUnit* intpart) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
UNIT_LIB_DEFAULT_TYPE intp;
dimensionless::scalar_t fracpart = dimensionless::scalar_t(std::modf(x(), &intp));
*intpart = intp;
return fracpart;
}
/**
* @ingroup UnitMath
* @brief Compute binary exponential function
* @details Returns the base-2 exponential function of x, which is 2 raised to the power x: 2^x.
* 2param[in] x Value of the exponent.
* @returns 2 raised to the power of x.
*/
template<class ScalarUnit>
dimensionless::scalar_t exp2(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return dimensionless::scalar_t(std::exp2(x()));
}
/**
* @ingroup UnitMath
* @brief Compute exponential minus one
* @details Returns e raised to the power x minus one: e^x-1. For small magnitude values
* of x, expm1 may be more accurate than exp(x)-1.
* @param[in] x Value of the exponent.
* @returns e raised to the power of x, minus one.
*/
template<class ScalarUnit>
dimensionless::scalar_t expm1(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return dimensionless::scalar_t(std::expm1(x()));
}
/**
* @ingroup UnitMath
* @brief Compute logarithm plus one
* @details Returns the natural logarithm of one plus x. For small magnitude values of
* x, logp1 may be more accurate than log(1+x).
* @param[in] x Value whose logarithm is calculated. If the argument is less than -1, a
* domain error occurs.
* @returns The natural logarithm of (1+x).
*/
template<class ScalarUnit>
dimensionless::scalar_t log1p(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return dimensionless::scalar_t(std::log1p(x()));
}
/**
* @ingroup UnitMath
* @brief Compute binary logarithm
* @details Returns the binary (base-2) logarithm of x.
* @param[in] x Value whose logarithm is calculated. If the argument is negative, a
* domain error occurs.
* @returns The binary logarithm of x: log2x.
*/
template<class ScalarUnit>
dimensionless::scalar_t log2(const ScalarUnit x) noexcept
{
static_assert(traits::is_dimensionless_unit<ScalarUnit>::value, "Type `ScalarUnit` must be a dimensionless unit derived from `unit_t`.");
return dimensionless::scalar_t(std::log2(x()));
}
//----------------------------------
// POWER FUNCTIONS
//----------------------------------
/* pow is implemented earlier in the library since a lot of the unit definitions depend on it */
/**
* @ingroup UnitMath
* @brief computes the square root of <i>value</i>
* @details Only implemented for linear_scale units.
* @param[in] value `unit_t` derived type to compute the square root of.
* @returns new unit_t, whose units are the square root of value's. E.g. if values
* had units of `square_meter`, then the return type will have units of
* `meter`.
* @note `sqrt` provides a _rational approximation_ of the square root of <i>value</i>.
* In some cases, _both_ the returned value _and_ conversion factor of the returned
* unit type may have errors no larger than `1e-10`.
*/
template<class UnitType, std::enable_if_t<units::traits::has_linear_scale<UnitType>::value, int> = 0>
inline auto sqrt(const UnitType& value) noexcept -> unit_t<square_root<typename units::traits::unit_t_traits<UnitType>::unit_type>, typename units::traits::unit_t_traits<UnitType>::underlying_type, linear_scale>
{
return unit_t<square_root<typename units::traits::unit_t_traits<UnitType>::unit_type>, typename units::traits::unit_t_traits<UnitType>::underlying_type, linear_scale>
(std::sqrt(value()));
}
/**
* @ingroup UnitMath
* @brief Computes the square root of the sum-of-squares of x and y.
* @details Only implemented for linear_scale units.
* @param[in] x unit_t type value
* @param[in] y unit_t type value
* @returns square root of the sum-of-squares of x and y in the same units
* as x.
*/
template<class UnitTypeLhs, class UnitTypeRhs, std::enable_if_t<units::traits::has_linear_scale<UnitTypeLhs, UnitTypeRhs>::value, int> = 0>
inline UnitTypeLhs hypot(const UnitTypeLhs& x, const UnitTypeRhs& y)
{
static_assert(traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value, "Parameters of hypot() function are not compatible units.");
return UnitTypeLhs(std::hypot(x(), y.template convert<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type>()()));
}
//----------------------------------
// ROUNDING FUNCTIONS
//----------------------------------
/**
* @ingroup UnitMath
* @brief Round up value
* @details Rounds x upward, returning the smallest integral value that is not less than x.
* @param[in] x Unit value to round up.
* @returns The smallest integral value that is not less than x.
*/
template<class UnitType, class = std::enable_if_t<traits::is_unit_t<UnitType>::value>>
UnitType ceil(const UnitType x) noexcept
{
return UnitType(std::ceil(x()));
}
/**
* @ingroup UnitMath
* @brief Round down value
* @details Rounds x downward, returning the largest integral value that is not greater than x.
* @param[in] x Unit value to round down.
* @returns The value of x rounded downward.
*/
template<class UnitType, class = std::enable_if_t<traits::is_unit_t<UnitType>::value>>
UnitType floor(const UnitType x) noexcept
{
return UnitType(std::floor(x()));
}
/**
* @ingroup UnitMath
* @brief Compute remainder of division
* @details Returns the floating-point remainder of numer/denom (rounded towards zero).
* @param[in] numer Value of the quotient numerator.
* @param[in] denom Value of the quotient denominator.
* @returns The remainder of dividing the arguments.
*/
template<class UnitTypeLhs, class UnitTypeRhs, class = std::enable_if_t<traits::is_unit_t<UnitTypeLhs>::value && traits::is_unit_t<UnitTypeRhs>::value>>
UnitTypeLhs fmod(const UnitTypeLhs numer, const UnitTypeRhs denom) noexcept
{
static_assert(traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value, "Parameters of fmod() function are not compatible units.");
return UnitTypeLhs(std::fmod(numer(), denom.template convert<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type>()()));
}
/**
* @ingroup UnitMath
* @brief Truncate value
* @details Rounds x toward zero, returning the nearest integral value that is not
* larger in magnitude than x. Effectively rounds towards 0.
* @param[in] x Value to truncate
* @returns The nearest integral value that is not larger in magnitude than x.
*/
template<class UnitType, class = std::enable_if_t<traits::is_unit_t<UnitType>::value>>
UnitType trunc(const UnitType x) noexcept
{
return UnitType(std::trunc(x()));
}
/**
* @ingroup UnitMath
* @brief Round to nearest
* @details Returns the integral value that is nearest to x, with halfway cases rounded
* away from zero.
* @param[in] x value to round.
* @returns The value of x rounded to the nearest integral.
*/
template<class UnitType, class = std::enable_if_t<traits::is_unit_t<UnitType>::value>>
UnitType round(const UnitType x) noexcept
{
return UnitType(std::round(x()));
}
//----------------------------------
// FLOATING POINT MANIPULATION
//----------------------------------
/**
* @ingroup UnitMath
* @brief Copy sign
* @details Returns a value with the magnitude and dimension of x, and the sign of y.
* Values x and y do not have to be compatible units.
* @param[in] x Value with the magnitude of the resulting value.
* @param[in] y Value with the sign of the resulting value.
* @returns value with the magnitude and dimension of x, and the sign of y.
*/
template<class UnitTypeLhs, class UnitTypeRhs, class = std::enable_if_t<traits::is_unit_t<UnitTypeLhs>::value && traits::is_unit_t<UnitTypeRhs>::value>>
UnitTypeLhs copysign(const UnitTypeLhs x, const UnitTypeRhs y) noexcept
{
return UnitTypeLhs(std::copysign(x(), y())); // no need for conversion to get the correct sign.
}
/// Overload to copy the sign from a raw double
template<class UnitTypeLhs, class = std::enable_if_t<traits::is_unit_t<UnitTypeLhs>::value>>
UnitTypeLhs copysign(const UnitTypeLhs x, const UNIT_LIB_DEFAULT_TYPE y) noexcept
{
return UnitTypeLhs(std::copysign(x(), y));
}
//----------------------------------
// MIN / MAX / DIFFERENCE
//----------------------------------
/**
* @ingroup UnitMath
* @brief Positive difference
* @details The function returns x-y if x>y, and zero otherwise, in the same units as x.
* Values x and y do not have to be the same type of units, but they do have to
* be compatible.
* @param[in] x Values whose difference is calculated.
* @param[in] y Values whose difference is calculated.
* @returns The positive difference between x and y.
*/
template<class UnitTypeLhs, class UnitTypeRhs, class = std::enable_if_t<traits::is_unit_t<UnitTypeLhs>::value && traits::is_unit_t<UnitTypeRhs>::value>>
UnitTypeLhs fdim(const UnitTypeLhs x, const UnitTypeRhs y) noexcept
{
static_assert(traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value, "Parameters of fdim() function are not compatible units.");
return UnitTypeLhs(std::fdim(x(), y.template convert<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type>()()));
}
/**
* @ingroup UnitMath
* @brief Maximum value
* @details Returns the larger of its arguments: either x or y, in the same units as x.
* Values x and y do not have to be the same type of units, but they do have to
* be compatible.
* @param[in] x Values among which the function selects a maximum.
* @param[in] y Values among which the function selects a maximum.
* @returns The maximum numeric value of its arguments.
*/
template<class UnitTypeLhs, class UnitTypeRhs, class = std::enable_if_t<traits::is_unit_t<UnitTypeLhs>::value && traits::is_unit_t<UnitTypeRhs>::value>>
UnitTypeLhs fmax(const UnitTypeLhs x, const UnitTypeRhs y) noexcept
{
static_assert(traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value, "Parameters of fmax() function are not compatible units.");
return UnitTypeLhs(std::fmax(x(), y.template convert<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type>()()));
}
/**
* @ingroup UnitMath
* @brief Minimum value
* @details Returns the smaller of its arguments: either x or y, in the same units as x.
* If one of the arguments in a NaN, the other is returned.
* Values x and y do not have to be the same type of units, but they do have to
* be compatible.
* @param[in] x Values among which the function selects a minimum.
* @param[in] y Values among which the function selects a minimum.
* @returns The minimum numeric value of its arguments.
*/
template<class UnitTypeLhs, class UnitTypeRhs, class = std::enable_if_t<traits::is_unit_t<UnitTypeLhs>::value && traits::is_unit_t<UnitTypeRhs>::value>>
UnitTypeLhs fmin(const UnitTypeLhs x, const UnitTypeRhs y) noexcept
{
static_assert(traits::is_convertible_unit_t<UnitTypeLhs, UnitTypeRhs>::value, "Parameters of fmin() function are not compatible units.");
return UnitTypeLhs(std::fmin(x(), y.template convert<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type>()()));
}
//----------------------------------
// OTHER FUNCTIONS
//----------------------------------
/**
* @ingroup UnitMath
* @brief Compute absolute value
* @details Returns the absolute value of x, i.e. |x|.
* @param[in] x Value whose absolute value is returned.
* @returns The absolute value of x.
*/
template<class UnitType, class = std::enable_if_t<traits::is_unit_t<UnitType>::value>>
UnitType fabs(const UnitType x) noexcept
{
return UnitType(std::fabs(x()));
}
/**
* @ingroup UnitMath
* @brief Compute absolute value
* @details Returns the absolute value of x, i.e. |x|.
* @param[in] x Value whose absolute value is returned.
* @returns The absolute value of x.
*/
template<class UnitType, class = std::enable_if_t<traits::is_unit_t<UnitType>::value>>
UnitType abs(const UnitType x) noexcept
{
return UnitType(std::fabs(x()));
}
/**
* @ingroup UnitMath
* @brief Multiply-add
* @details Returns x*y+z. The function computes the result without losing precision in
* any intermediate result. The resulting unit type is a compound unit of x* y.
* @param[in] x Values to be multiplied.
* @param[in] y Values to be multiplied.
* @param[in] z Value to be added.
* @returns The result of x*y+z
*/
template<class UnitTypeLhs, class UnitMultiply, class UnitAdd, class = std::enable_if_t<traits::is_unit_t<UnitTypeLhs>::value && traits::is_unit_t<UnitMultiply>::value && traits::is_unit_t<UnitAdd>::value>>
auto fma(const UnitTypeLhs x, const UnitMultiply y, const UnitAdd z) noexcept -> decltype(x * y)
{
using resultType = decltype(x * y);
static_assert(traits::is_convertible_unit_t<compound_unit<typename units::traits::unit_t_traits<UnitTypeLhs>::unit_type, typename units::traits::unit_t_traits<UnitMultiply>::unit_type>, typename units::traits::unit_t_traits<UnitAdd>::unit_type>::value, "Unit types are not compatible.");
return resultType(std::fma(x(), y(), resultType(z)()));
}
} // end namespace math
} // end namespace units
//------------------------------
// std::numeric_limits
//------------------------------
namespace std
{
template<class Units, typename T, template<typename> class NonLinearScale>
class numeric_limits<units::unit_t<Units, T, NonLinearScale>>
{
public:
static constexpr units::unit_t<Units, T, NonLinearScale> min()
{
return units::unit_t<Units, T, NonLinearScale>(std::numeric_limits<T>::min());
}
static constexpr units::unit_t<Units, T, NonLinearScale> max()
{
return units::unit_t<Units, T, NonLinearScale>(std::numeric_limits<T>::max());
}
static constexpr units::unit_t<Units, T, NonLinearScale> lowest()
{
return units::unit_t<Units, T, NonLinearScale>(std::numeric_limits<T>::lowest());
}
};
}
#ifdef _MSC_VER
# if _MSC_VER <= 1800
# pragma warning(pop)
# undef constexpr
# pragma pop_macro("constexpr")
# undef noexcept
# pragma pop_macro("noexcept")
# undef _ALLOW_KEYWORD_MACROS
# endif // _MSC_VER < 1800
# pragma pop_macro("pascal")
#endif // _MSC_VER
#endif // units_h__
// For Emacs
// Local Variables:
// Mode: C++
// c-basic-offset: 2
// fill-column: 116
// tab-width: 4
// End:
using namespace units::literals;
namespace units {
using namespace length;
using namespace time;
using namespace velocity;
using namespace acceleration;
using namespace angular_velocity;
} // namespace units
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