Implementation of Math's API's unit system. More...

#include <iostream>
#include <ratio>
#include <Utility/String/NRE_String.hpp>
#include <Utility/Interfaces/Stringable/NRE_Stringable.hpp>
#include "NRE_Math.hpp"

Go to the source code of this file.

Classes
class	NRE::Math::Unit< M, L, T, A >
	Used to define clear physical unit. More...

Namespaces
	NRE
	The NearlyRealEngine's global namespace.

	Math
	Math's API.

Macros
#define	TYPEDEF_UNIT(M, L, T, A, name) typedef Unit<std::ratio<M>, std::ratio<L>, std::ratio<T>, std::ratio<A>> name

Functions
template<class M , class L , class T , class A >
std::ostream &	NRE::Math::operator<< (std::ostream &stream, Unit< M, L, T, A > const &o)

template<class M , class L , class T , class A , class M2 , class L2 , class T2 , class A2 >
constexpr Unit< std::ratio_subtract< M, M2 >, std::ratio_subtract< L, L2 >, std::ratio_subtract< T, T2 >, std::ratio_subtract< A, A2 > >	NRE::Math::operator/ (Unit< M, L, T, A > const &u1, Unit< M2, L2, T2, A2 > const &u2)

template<class M , class L , class T , class A >
constexpr Unit< std::ratio_subtract< std::ratio< 0 >, M >, std::ratio_subtract< std::ratio< 0 >, L >, std::ratio_subtract< std::ratio< 0 >, T >, std::ratio_subtract< std::ratio< 0 >, A > >	NRE::Math::operator/ (long double x, Unit< M, L, T, A > const &u)

template<class M , class L , class T , class A >
constexpr Unit< M, L, T, A >	NRE::Math::operator/ (Unit< M, L, T, A > const &u, long double x)

template<class M , class L , class T , class A , class M2 , class L2 , class T2 , class A2 >
constexpr Unit< std::ratio_add< M, M2 >, std::ratio_add< L, L2 >, std::ratio_add< T, T2 >, std::ratio_add< A, A2 > >	NRE::Math::operator* (Unit< M, L, T, A > const &u1, Unit< M2, L2, T2, A2 > const &u2)

template<class M , class L , class T , class A >
constexpr Unit< M, L, T, A >	NRE::Math::operator* (long double x, Unit< M, L, T, A > const &u)

template<class M , class L , class T , class A >
constexpr Unit< M, L, T, A >	NRE::Math::operator* (Unit< M, L, T, A > const &u, long double x)

	NRE::Math::TYPEDEF_UNIT (1, 0, 0, 0, UMass)

	NRE::Math::TYPEDEF_UNIT (0, 1, 0, 0, ULength)

	NRE::Math::TYPEDEF_UNIT (0, 2, 0, 0, UArea)

	NRE::Math::TYPEDEF_UNIT (0, 3, 0, 0, UVolume)

	NRE::Math::TYPEDEF_UNIT (0, 0, 1, 0, UTime)

	NRE::Math::TYPEDEF_UNIT (0, 1,-1, 0, USpeed)

	NRE::Math::TYPEDEF_UNIT (0, 1,-2, 0, UAcceleration)

	NRE::Math::TYPEDEF_UNIT (0, 0,-1, 0, UFrequency)

	NRE::Math::TYPEDEF_UNIT (1, 1,-2, 0, UForce)

	NRE::Math::TYPEDEF_UNIT (1,-1,-2, 0, UPressure)

	NRE::Math::TYPEDEF_UNIT (0, 0, 0, 1, Angle)

constexpr UMass	NRE::Math::kilogramme (1.0)

constexpr ULength	NRE::Math::metre (1.0)

constexpr UTime	NRE::Math::second (1.0)

constexpr UFrequency	NRE::Math::Hz (1.0)

constexpr UForce	NRE::Math::newton (1.0)

constexpr UPressure	NRE::Math::pascal (1.0)

constexpr ULength	NRE::Math::operator""_mm (long double x)

constexpr ULength	NRE::Math::operator""_cm (long double x)

constexpr ULength	NRE::Math::operator""_m (long double x)

constexpr ULength	NRE::Math::operator""_km (long double x)

constexpr ULength	NRE::Math::operator""_mm (unsigned long long int x)

constexpr ULength	NRE::Math::operator""_cm (unsigned long long int x)

constexpr ULength	NRE::Math::operator""_m (unsigned long long int x)

constexpr ULength	NRE::Math::operator""_km (unsigned long long int x)

constexpr USpeed	NRE::Math::operator""_kmph (long double x)

constexpr USpeed	NRE::Math::operator""_kmph (unsigned long long int x)

constexpr UFrequency	NRE::Math::operator""_Hz (long double x)

constexpr UFrequency	NRE::Math::operator""_Hz (unsigned long long int x)

constexpr UTime	NRE::Math::operator""_s (long double x)

constexpr UTime	NRE::Math::operator""_min (long double x)

constexpr UTime	NRE::Math::operator""_h (long double x)

constexpr UTime	NRE::Math::operator""_day (long double x)

constexpr UTime	NRE::Math::operator""_s (unsigned long long int x)

constexpr UTime	NRE::Math::operator""_min (unsigned long long int x)

constexpr UTime	NRE::Math::operator""_h (unsigned long long int x)

constexpr UTime	NRE::Math::operator""_day (unsigned long long int x)

constexpr UMass	NRE::Math::operator""_kg (long double x)

constexpr UMass	NRE::Math::operator""_g (long double x)

constexpr UMass	NRE::Math::operator""_t (long double x)

constexpr UMass	NRE::Math::operator""_kg (unsigned long long int x)

constexpr UMass	NRE::Math::operator""_g (unsigned long long int x)

constexpr UMass	NRE::Math::operator""_t (unsigned long long int x)

constexpr UAcceleration	NRE::Math::operator""_mps2 (long double x)

constexpr UAcceleration	NRE::Math::operator""_mps2 (unsigned long long int x)

constexpr UAcceleration	NRE::Math::operator""_G (long double x)

constexpr UAcceleration	NRE::Math::operator""_G (unsigned long long int x)

constexpr UForce	NRE::Math::operator""_N (long double x)

constexpr UForce	NRE::Math::operator""_N (unsigned long long int x)

constexpr UPressure	NRE::Math::operator""_Pa (long double x)

constexpr UPressure	NRE::Math::operator""_Pa (unsigned long long int x)

constexpr long double	NRE::Math::operator""_pi (long double x)

constexpr long double	NRE::Math::operator""_pi (unsigned long long int x)

constexpr Angle	NRE::Math::radian (1.0)

constexpr Angle	NRE::Math::operator""_rad (long double x)

constexpr Angle	NRE::Math::operator""_rad (unsigned long long int x)

constexpr Angle	NRE::Math::operator""_deg (long double x)

constexpr Angle	NRE::Math::operator""_deg (unsigned long long int x)

double	NRE::Math::sin (Angle const &u)

double	NRE::Math::cos (Angle const &u)

double	NRE::Math::tan (Angle const &u)

double	NRE::Math::asin (Angle const &u)

double	NRE::Math::acos (Angle const &u)

double	NRE::Math::atan (Angle const &u)

double	NRE::Math::toRad (Angle const &u)

double	NRE::Math::toDeg (Angle const &u)

Variables
constexpr UMass	NRE::Math::gramme = 0.001 * kilogramme

constexpr UMass	NRE::Math::tonne = 1000 * kilogramme

constexpr ULength	NRE::Math::decimetre = metre / 10

constexpr ULength	NRE::Math::centimetre = metre / 100

constexpr ULength	NRE::Math::millimetre = metre / 1000

constexpr ULength	NRE::Math::kilometre = 1000 * metre

constexpr UArea	NRE::Math::metre2 = metre * metre

constexpr UArea	NRE::Math::decimetre2 = decimetre * decimetre

constexpr UArea	NRE::Math::centimetre2 = centimetre * centimetre

constexpr UArea	NRE::Math::millimetre2 = millimetre * millimetre

constexpr UArea	NRE::Math::kilometre2 = kilometre * kilometre

constexpr UVolume	NRE::Math::metre3 = metre2 * metre

constexpr UVolume	NRE::Math::decimetre3 = decimetre2 * decimetre

constexpr UVolume	NRE::Math::centimetre3 = centimetre2 * centimetre

constexpr UVolume	NRE::Math::millimetre3 = millimetre2 * millimetre

constexpr UVolume	NRE::Math::kilometre3 = kilometre2 * kilometre

constexpr UVolume	NRE::Math::litre = decimetre3

constexpr UTime	NRE::Math::minute = 60 * second

constexpr UTime	NRE::Math::hour = 60 * minute

constexpr UTime	NRE::Math::day = 24 * hour

constexpr UAcceleration	NRE::Math::G = 9.80665 * metre / (second * second)

constexpr Angle	NRE::Math::degree = (PI / 180.0f) * radian

Detailed Description

Implementation of Math's API's unit system.

Author: Louis ABEL

Date: 08/09/2018

Copyright: CC-BY-NC-SA

Macro Definition Documentation

#define TYPEDEF_UNIT	(	M,
		L,
		T,
		A,
		name
	)	typedef Unit<std::ratio<M>, std::ratio<L>, std::ratio<T>, std::ratio<A>> name

Mass unit

Function Documentation

double NRE::Math::acos ( Angle const & u )

inline

Compute the arc cos of a unit in typed manners

Parameters

u the unit

Returns: the resulting tan

double NRE::Math::asin ( Angle const & u )

inline

Compute the arc sin of a unit in typed manners

Parameters

u the unit

Returns: the resulting tan

double NRE::Math::atan ( Angle const & u )

inline

Compute the arc tan of a unit in typed manners

Parameters

u the unit

Returns: the resulting tan

double NRE::Math::cos ( Angle const & u )

inline

Compute the cos of a unit in typed manners

Parameters

u the unit

Returns: the resulting cos

constexpr UFrequency NRE::Math::Hz ( 1. 0 )

Standard SI unit

constexpr UMass NRE::Math::kilogramme ( 1. 0 )

Standard SI unit

constexpr ULength NRE::Math::metre ( 1. 0 )

Standard SI unit

constexpr UForce NRE::Math::newton ( 1. 0 )

Standard SI unit

constexpr ULength NRE::Math::operator""_cm ( long double x )

Litteral operator for centimetre

Parameters

x	the value to convert

Returns: the corresponding length

constexpr ULength NRE::Math::operator""_cm ( unsigned long long int x )

Litteral operator for centimetre

Parameters

x	the value to convert

Returns: the corresponding length

constexpr UTime NRE::Math::operator""_day ( long double x )

Litteral operator for day

Parameters

x	the value to convert

Returns: the corresponding time

constexpr UTime NRE::Math::operator""_day ( unsigned long long int x )

Litteral operator for day

Parameters

x	the value to convert

Returns: the corresponding time

constexpr Angle NRE::Math::operator""_deg ( long double x )

Litteral operator for degree

Parameters

x	the value to convert

Returns: the corresponding angle

constexpr Angle NRE::Math::operator""_deg ( unsigned long long int x )

Litteral operator for degree

Parameters

x	the value to convert

Returns: the corresponding angle

constexpr UMass NRE::Math::operator""_g ( long double x )

Litteral operator for gramme

Parameters

x	the value to convert

Returns: the corresponding mass

constexpr UMass NRE::Math::operator""_g ( unsigned long long int x )

Litteral operator for gramme

Parameters

x	the value to convert

Returns: the corresponding mass

constexpr UAcceleration NRE::Math::operator""_G ( long double x )

Litteral operator for gravity

Parameters

x	the value to convert

Returns: the corresponding acceleration

constexpr UAcceleration NRE::Math::operator""_G ( unsigned long long int x )

Litteral operator for gravity

Parameters

x	the value to convert

Returns: the corresponding acceleration

constexpr UTime NRE::Math::operator""_h ( long double x )

Litteral operator for hour

Parameters

x	the value to convert

Returns: the corresponding time

constexpr UTime NRE::Math::operator""_h ( unsigned long long int x )

Litteral operator for hour

Parameters

x	the value to convert

Returns: the corresponding time

constexpr UFrequency NRE::Math::operator""_Hz ( long double x )

Litteral operator for hertz

Parameters

x	the value to convert

Returns: the corresponding frequency

constexpr UFrequency NRE::Math::operator""_Hz ( unsigned long long int x )

Litteral operator for hertz

Parameters

x	the value to convert

Returns: the corresponding frequency

constexpr UMass NRE::Math::operator""_kg ( long double x )

Litteral operator for kilogramme

Parameters

x	the value to convert

Returns: the corresponding mass

constexpr UMass NRE::Math::operator""_kg ( unsigned long long int x )

Litteral operator for kilogramme

Parameters

x	the value to convert

Returns: the corresponding mass

constexpr ULength NRE::Math::operator""_km ( long double x )

Litteral operator for kilometre

Parameters

x	the value to convert

Returns: the corresponding length

constexpr ULength NRE::Math::operator""_km ( unsigned long long int x )

Litteral operator for kilometre

Parameters

x	the value to convert

Returns: the corresponding length

constexpr USpeed NRE::Math::operator""_kmph ( long double x )

Litteral operator for kilometre per hour

Parameters

x	the value to convert

Returns: the corresponding speed

constexpr USpeed NRE::Math::operator""_kmph ( unsigned long long int x )

Litteral operator for kilometre per hour

Parameters

x	the value to convert

Returns: the corresponding speed

constexpr ULength NRE::Math::operator""_m ( long double x )

Litteral operator for metre

Parameters

x	the value to convert

Returns: the corresponding length

constexpr ULength NRE::Math::operator""_m ( unsigned long long int x )

Litteral operator for metre

Parameters

x	the value to convert

Returns: the corresponding length

constexpr UTime NRE::Math::operator""_min ( long double x )

Litteral operator for minute

Parameters

x	the value to convert

Returns: the corresponding time

constexpr UTime NRE::Math::operator""_min ( unsigned long long int x )

Litteral operator for minute

Parameters

x	the value to convert

Returns: the corresponding time

constexpr ULength NRE::Math::operator""_mm ( long double x )

Litteral operator for millimetre

Parameters

x	the value to convert

Returns: the corresponding length

constexpr ULength NRE::Math::operator""_mm ( unsigned long long int x )

Litteral operator for millimetre

Parameters

x	the value to convert

Returns: the corresponding length

constexpr UAcceleration NRE::Math::operator""_mps2 ( long double x )

Litteral operator for metre per second square

Parameters

x	the value to convert

Returns: the corresponding acceleration

constexpr UAcceleration NRE::Math::operator""_mps2 ( unsigned long long int x )

Litteral operator for metre per second square

Parameters

x	the value to convert

Returns: the corresponding acceleration

constexpr UForce NRE::Math::operator""_N ( long double x )

Litteral operator for newton

Parameters

x	the value to convert

Returns: the corresponding force

constexpr UForce NRE::Math::operator""_N ( unsigned long long int x )

Litteral operator for newton

Parameters

x	the value to convert

Returns: the corresponding force

constexpr UPressure NRE::Math::operator""_Pa ( long double x )

Litteral operator for pascal

Parameters

x	the value to convert

Returns: the corresponding pressure

constexpr UPressure NRE::Math::operator""_Pa ( unsigned long long int x )

Litteral operator for pascal

Parameters

x	the value to convert

Returns: the corresponding pressure

constexpr long double NRE::Math::operator""_pi ( long double x )

Litteral operator for pi

Parameters

x	the value to convert

Returns: the corresponding value

constexpr long double NRE::Math::operator""_pi ( unsigned long long int x )

Litteral operator for pi

Parameters

x	the value to convert

Returns: the corresponding value

constexpr Angle NRE::Math::operator""_rad ( long double x )

Litteral operator for radian

Parameters

x	the value to convert

Returns: the corresponding angle

constexpr Angle NRE::Math::operator""_rad ( unsigned long long int x )

Litteral operator for radian

Parameters

x	the value to convert

Returns: the corresponding angle

constexpr UTime NRE::Math::operator""_s ( long double x )

Litteral operator for second

Parameters

x	the value to convert

Returns: the corresponding time

constexpr UTime NRE::Math::operator""_s ( unsigned long long int x )

Litteral operator for second

Parameters

x	the value to convert

Returns: the corresponding time

constexpr UMass NRE::Math::operator""_t ( long double x )

Litteral operator for tonne

Parameters

x	the value to convert

Returns: the corresponding mass

constexpr UMass NRE::Math::operator""_t ( unsigned long long int x )

Litteral operator for tonne

Parameters

x	the value to convert

Returns: the corresponding mass

template<class M , class L , class T , class A , class M2 , class L2 , class T2 , class A2 >

constexpr Unit<std::ratio_add<M, M2>, std::ratio_add<L, L2>, std::ratio_add<T, T2>, std::ratio_add<A, A2> > NRE::Math::operator*	(	Unit< M, L, T, A > const &	u1,
		Unit< M2, L2, T2, A2 > const &	u2
	)

Compute the unit resulting in the multiplication of u1 by u2

Parameters

u1	the first unit
u2	the second unit

Returns: the computed unit

template<class M , class L , class T , class A >

constexpr Unit<M, L, T, A> NRE::Math::operator*	(	long double	x,
		Unit< M, L, T, A > const &	u
	)

Compute the unit resulting in the multiplication of x by u

Parameters

x	the value to multiply with u
u	the unit

Returns: the computed unit

template<class M , class L , class T , class A >

constexpr Unit<M, L, T, A> NRE::Math::operator*	(	Unit< M, L, T, A > const &	u,
		long double	x
	)

Compute the unit resulting in the multiplication of u by x

Parameters

u	the unit
x	the value to multiply with u

Returns: the computed unitUsed to create a new standard unit

template<class M , class L , class T , class A , class M2 , class L2 , class T2 , class A2 >

constexpr Unit<std::ratio_subtract<M, M2>, std::ratio_subtract<L, L2>, std::ratio_subtract<T, T2>, std::ratio_subtract<A, A2> > NRE::Math::operator/	(	Unit< M, L, T, A > const &	u1,
		Unit< M2, L2, T2, A2 > const &	u2
	)

Compute the unit resulting in the division of u1 by u2

Parameters

u1	the first unit
u2	the second unit

Returns: the computed unit

template<class M , class L , class T , class A >

constexpr Unit<std::ratio_subtract<std::ratio<0>, M>, std::ratio_subtract<std::ratio<0>, L>, std::ratio_subtract<std::ratio<0>, T>, std::ratio_subtract<std::ratio<0>, A> > NRE::Math::operator/	(	long double	x,
		Unit< M, L, T, A > const &	u
	)

Compute the unit resulting in the division of x by u

Parameters

x	the value to divide with u
u	the unit

Returns: the computed unit

template<class M , class L , class T , class A >

constexpr Unit<M, L, T, A> NRE::Math::operator/	(	Unit< M, L, T, A > const &	u,
		long double	x
	)

Compute the unit resulting in the division of u by x

Parameters

u	the unit to be divided
x	the value

Returns: the computed unit

template<class M , class L , class T , class A >

std::ostream& NRE::Math::operator<<	(	std::ostream &	stream,
		Unit< M, L, T, A > const &	o
	)

Output stream operator for the object

Parameters

stream	the stream to add the object's string representation
o	the object to add in the stream

Returns: the modified stream

constexpr UPressure NRE::Math::pascal ( 1. 0 )

Standard SI unit

constexpr Angle NRE::Math::radian ( 1. 0 )

Standard SI unit

constexpr UTime NRE::Math::second ( 1. 0 )

Standard SI unit

double NRE::Math::sin ( Angle const & u )

inline

Compute the sin of a unit in typed manners

Parameters

u the unit

Returns: the resulting sin

double NRE::Math::tan ( Angle const & u )

inline

Compute the tan of a unit in typed manners

Parameters

u the unit

Returns: the resulting tan

double NRE::Math::toDeg ( Angle const & u )

inline

Return the angle value in degree

Parameters

u the unit

Returns: the resulting angle

double NRE::Math::toRad ( Angle const & u )

inline

Return the angle value in radian

Parameters

u the unit

Returns: the resulting angle

NRE::Math::TYPEDEF_UNIT	(	1	,
		0	,
		0	,
		0	,
		UMass
	)

Length unit

NRE::Math::TYPEDEF_UNIT	(	0	,
		1	,
		0	,
		0	,
		ULength
	)

Area unit

NRE::Math::TYPEDEF_UNIT	(	0	,
		2	,
		0	,
		0	,
		UArea
	)

Volume unit

NRE::Math::TYPEDEF_UNIT	(	0	,
		3	,
		0	,
		0	,
		UVolume
	)

Time unit

NRE::Math::TYPEDEF_UNIT	(	0	,
		0	,
		1	,
		0	,
		UTime
	)

Speed unit

NRE::Math::TYPEDEF_UNIT	(	0	,
		1	,
		-	1,
		0	,
		USpeed
	)

Acceleration unit

NRE::Math::TYPEDEF_UNIT	(	0	,
		1	,
		-	2,
		0	,
		UAcceleration
	)

Frequency unit

NRE::Math::TYPEDEF_UNIT	(	0	,
		0	,
		-	1,
		0	,
		UFrequency
	)

Force unit

NRE::Math::TYPEDEF_UNIT	(	1	,
		1	,
		-	2,
		0	,
		UForce
	)

Pressure unit

NRE::Math::TYPEDEF_UNIT	(	1	,
		-	1,
		-	2,
		0	,
		UPressure
	)

Angle unit

Variable Documentation

constexpr ULength NRE::Math::centimetre = metre / 100

A hundredth of metre

constexpr UArea NRE::Math::centimetre2 = centimetre * centimetre

One by One centimetre square

constexpr UVolume NRE::Math::centimetre3 = centimetre2 * centimetre

One by One by One centimetre cube

constexpr UTime NRE::Math::day = 24 * hour

Twenty four hours

constexpr ULength NRE::Math::decimetre = metre / 10

A tenth of metre

constexpr UArea NRE::Math::decimetre2 = decimetre * decimetre

One by One decimetre square

constexpr UVolume NRE::Math::decimetre3 = decimetre2 * decimetre

One by One by One decimetre cube

constexpr Angle NRE::Math::degree = (PI / 180.0f) * radian

Scale degree with radian

constexpr UAcceleration NRE::Math::G = 9.80665 * metre / (second * second)

Standard Gravity value

constexpr UMass NRE::Math::gramme = 0.001 * kilogramme

A thousandth of kilogramme

constexpr UTime NRE::Math::hour = 60 * minute

Sixty minutes

constexpr ULength NRE::Math::kilometre = 1000 * metre

One thousand of metre

constexpr UArea NRE::Math::kilometre2 = kilometre * kilometre

One by One kilometre square

constexpr UVolume NRE::Math::kilometre3 = kilometre2 * kilometre

One by One by One kilometre cube

constexpr UVolume NRE::Math::litre = decimetre3

One by One by One decimetre cube

constexpr UArea NRE::Math::metre2 = metre * metre

One by One metre square

constexpr UVolume NRE::Math::metre3 = metre2 * metre

One by One by One metre cube

constexpr ULength NRE::Math::millimetre = metre / 1000

A thousandth of metre

constexpr UArea NRE::Math::millimetre2 = millimetre * millimetre

One by One millimetre square

constexpr UVolume NRE::Math::millimetre3 = millimetre2 * millimetre

One by One by One millimetre cube

constexpr UTime NRE::Math::minute = 60 * second

Sixty seconds

constexpr UMass NRE::Math::tonne = 1000 * kilogramme

One thousand of kilogramme

Classes

Namespaces

Macros

Functions

Variables

Detailed Description

Macro Definition Documentation

Function Documentation

Variable Documentation