Contains the rational class definition. More...

#include "array.h"
#include "bifstream.h"
#include "bofstream.h"
#include "math_funcs.h"
#include "matpack.h"
#include <ostream>

Classes
class	Rational
	Implements rational numbers to work with other ARTS types. More...

Macros
#define	RATIONAL_UNDEFINED Rational(0, 0)

Typedefs
using	ArrayOfRational = Array< Rational >

Functions
constexpr Index	gcd (Index a, Index b) noexcept
	Returns the greatest common denominator of two numbers. More...

constexpr Rational	reduce_by_gcd (const Rational a) noexcept
	Returns the rational reduced by the greates. More...

constexpr Rational	numeric2rational (Numeric x, size_t maxdec=4) noexcept
	Rational from Numeric. More...

constexpr Rational	operator- (const Rational a) noexcept
	Negative. More...

constexpr Rational	operator+ (const Rational a) noexcept
	Positive. More...

constexpr Rational	operator+ (const Rational a, const Rational b) noexcept
	Addition. More...

constexpr Rational	operator+ (const Rational a, Index b) noexcept
	Addition. More...

constexpr Rational	operator+ (const Rational a, int b) noexcept
	Addition. More...

constexpr Rational	operator+ (Index b, const Rational a) noexcept
	Addition. More...

constexpr Rational	operator+ (int b, const Rational a) noexcept
	Addition. More...

constexpr Rational	operator- (const Rational a, const Rational b) noexcept
	Subtraction. More...

constexpr Rational	operator- (const Rational a, Index b) noexcept
	Subtraction. More...

constexpr Rational	operator- (const Rational a, int b) noexcept
	Subtraction. More...

constexpr Rational	operator- (Index b, const Rational a) noexcept
	Subtraction. More...

constexpr Rational	operator- (int b, const Rational a) noexcept
	Subtraction. More...

constexpr Rational	operator/ (const Rational a, const Rational b) noexcept
	Division. More...

constexpr Rational	operator/ (const Rational a, Index b) noexcept
	Division. More...

constexpr Rational	operator/ (const Rational a, int b) noexcept
	Division. More...

constexpr Rational	operator/ (Index b, const Rational a) noexcept
	Division. More...

constexpr Rational	operator/ (int b, const Rational a) noexcept
	Division. More...

constexpr Rational	operator* (const Rational a, const Rational b) noexcept
	Multiplication. More...

constexpr Rational	operator* (const Rational a, Index b) noexcept
	Multiplication. More...

constexpr Rational	operator* (const Rational a, int b) noexcept
	Multiplication. More...

constexpr Rational	operator* (Index b, const Rational a) noexcept
	Multiplication. More...

constexpr Rational	operator* (int b, const Rational a) noexcept
	Multiplication. More...

constexpr Rational	operator% (const Rational a, const Rational b) noexcept
	Remainder. More...

constexpr Rational	operator% (const Rational a, Index b) noexcept
	Remainder. More...

constexpr Rational	operator% (const Rational a, int b) noexcept
	Remainder. More...

constexpr Rational	operator% (Index b, const Rational a) noexcept
	Remainder. More...

constexpr Rational	operator% (int b, const Rational a) noexcept
	Remainder. More...

constexpr bool	operator== (const Rational a, const Rational b) noexcept
	Equality. More...

constexpr bool	operator!= (const Rational a, const Rational b) noexcept
	Inequality. More...

constexpr bool	operator< (const Rational a, const Rational b) noexcept
	Less than. More...

constexpr bool	operator> (const Rational a, const Rational b) noexcept
	More than. More...

constexpr bool	operator<= (const Rational a, const Rational b) noexcept
	Less than or equal to. More...

constexpr bool	operator>= (const Rational a, const Rational b) noexcept
	More than or equal to. More...

constexpr bool	operator! (const Rational a) noexcept
	Not. More...

Numeric	sqrt (const Rational r)
	Square root. More...

Numeric	pow (const Rational base, Numeric exp)
	Power of. More...

Numeric	pow (Numeric base, const Rational exp)
	Power of. More...

Numeric	pow (const Rational base, const Rational exp)
	Power of. More...

std::ostream &	operator<< (std::ostream &os, const Rational &a)
	Output operator. More...

std::istream &	operator>> (std::istream &is, Rational &a)
	Input operator. More...

constexpr bool	operator< (const Index a, const Rational b) noexcept
	less More...

constexpr bool	operator< (const int a, const Rational b) noexcept
	less More...

constexpr bool	operator< (const Rational a, const Index b) noexcept
	less More...

constexpr bool	operator< (const Rational a, const int b) noexcept
	less More...

constexpr bool	operator> (const Index a, const Rational b) noexcept
	more More...

constexpr bool	operator> (const int a, const Rational b) noexcept
	more More...

constexpr bool	operator> (const Rational a, const Index b) noexcept
	more More...

constexpr bool	operator> (const Rational a, const int b) noexcept
	more More...

constexpr bool	operator== (const Rational a, const Index b) noexcept
	equal More...

constexpr bool	operator== (const Rational a, const int b) noexcept
	equal More...

constexpr bool	operator!= (const Rational a, const Index b) noexcept
	not equal More...

constexpr bool	operator!= (const Rational a, const int b) noexcept
	not equal More...

constexpr Rational	abs (const Rational a) noexcept
	Absolute. More...

constexpr Rational	max (const Rational a, const Rational b) noexcept
	Maximum. More...

constexpr Rational	min (const Rational a, const Rational b) noexcept
	Minimum. More...

constexpr Rational	operator""_2 (unsigned long long int n) noexcept
	Returns common operator n/2. More...

constexpr bool	iseven (const Rational r) noexcept
	Returns true if even integer. More...

Detailed Description

Contains the rational class definition.

Author: Richard Larsson

Date: 2012-10-31

Definition in file rational.h.

Macro Definition Documentation

◆ RATIONAL_UNDEFINED

#define RATIONAL_UNDEFINED Rational(0, 0)

Definition at line 391 of file rational.h.

Typedef Documentation

◆ ArrayOfRational

using ArrayOfRational = Array<Rational>

Definition at line 926 of file rational.h.

Function Documentation

◆ abs()

constexpr Rational abs ( const Rational a )

constexprnoexcept

Absolute.

Parameters

[in] a Any Rational

Returns: constexpr Rational Absolute value of the Rational

Definition at line 902 of file rational.h.

References a.

◆ gcd()

constexpr Index gcd	(	Index	a,
		Index	b
	)

constexprnoexcept

Returns the greatest common denominator of two numbers.

Parameters

[in]	a	number a
[in]	b	number b

Returns: num such that Rational(a/num, b/num) is the same as Rational(a, b)

Definition at line 44 of file rational.h.

References a, b, and gcd().

Referenced by gcd(), Rational::Rational(), and reduce_by_gcd().

◆ iseven()

constexpr bool iseven ( const Rational r )

constexprnoexcept

Returns true if even integer.

Parameters

[in] r Any rational

Returns: true if r is even, otherwise false

Definition at line 942 of file rational.h.

Referenced by Absorption::LineMixing::Makarov2020etal::reduced_dipole(), and Absorption::reduced_magnetic_quadrapole().

◆ max()

constexpr Rational max	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Maximum.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: constexpr Rational Largest of a and b

Definition at line 912 of file rational.h.

References a, and b.

◆ min()

constexpr Rational min	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Minimum.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: constexpr Rational Smallest of a and b

Definition at line 922 of file rational.h.

References a, and b.

◆ numeric2rational()

constexpr Rational numeric2rational	(	Numeric	x,
		size_t	maxdec = `4`
	)

constexprnoexcept

Rational from Numeric.

Performs basic rounding

Parameters

[in]	x	Numeric value
[in]	maxdec	Maximum number of decimals

Definition at line 361 of file rational.h.

Referenced by Rational::Rational(), and test_numeric2rational().

◆ operator!()

constexpr bool operator! ( const Rational a )

constexprnoexcept

Not.

Parameters

[in] a Any Rational

Returns: true If a.Nom() and a.isDefined(); false Otherwise

Definition at line 732 of file rational.h.

References a.

◆ operator!=() [1/3]

constexpr bool operator!=	(	const Rational	a,
		const Index	b
	)

constexprnoexcept

not equal

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: True if a is not equal to b

Definition at line 883 of file rational.h.

References a, and b.

◆ operator!=() [2/3]

constexpr bool operator!=	(	const Rational	a,
		const int	b
	)

constexprnoexcept

not equal

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: True if a is not equal to b

Definition at line 893 of file rational.h.

References a, and b.

◆ operator!=() [3/3]

constexpr bool operator!=	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Inequality.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: true If not equal; false Otherwise

Definition at line 679 of file rational.h.

References a, and b.

◆ operator""_2()

constexpr Rational operator""_2 ( unsigned long long int n )

constexprnoexcept

Returns common operator n/2.

Parameters

[in] n Any positive integer

Returns: Rational(n, 2)

Definition at line 933 of file rational.h.

◆ operator%() [1/5]

constexpr Rational operator%	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Remainder.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: constexpr Rational a % b

Definition at line 613 of file rational.h.

References a, and b.

◆ operator%() [2/5]

constexpr Rational operator%	(	const Rational	a,
		Index	b
	)

constexprnoexcept

Remainder.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a % b

Definition at line 626 of file rational.h.

References a, and b.

◆ operator%() [3/5]

constexpr Rational operator%	(	const Rational	a,
		int	b
	)

constexprnoexcept

Remainder.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a % b

Definition at line 636 of file rational.h.

References a, and b.

◆ operator%() [4/5]

constexpr Rational operator%	(	Index	b,
		const Rational	a
	)

constexprnoexcept

Remainder.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational b % a

Definition at line 646 of file rational.h.

References a, and b.

◆ operator%() [5/5]

constexpr Rational operator%	(	int	b,
		const Rational	a
	)

constexprnoexcept

Remainder.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational b % a

Definition at line 656 of file rational.h.

References a, and b.

◆ operator*() [1/5]

constexpr Rational operator*	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Multiplication.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: constexpr Rational a * b

Definition at line 567 of file rational.h.

References a, and b.

Referenced by operator*().

◆ operator*() [2/5]

constexpr Rational operator*	(	const Rational	a,
		Index	b
	)

constexprnoexcept

Multiplication.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a * b

Definition at line 577 of file rational.h.

References a, and b.

◆ operator*() [3/5]

constexpr Rational operator*	(	const Rational	a,
		int	b
	)

constexprnoexcept

Multiplication.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a * b

Definition at line 587 of file rational.h.

References a, and b.

◆ operator*() [4/5]

constexpr Rational operator*	(	Index	b,
		const Rational	a
	)

constexprnoexcept

Multiplication.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational a * b

Definition at line 597 of file rational.h.

References a, b, and operator*().

◆ operator*() [5/5]

constexpr Rational operator*	(	int	b,
		const Rational	a
	)

constexprnoexcept

Multiplication.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational a * b

Definition at line 605 of file rational.h.

References a, b, and operator*().

◆ operator+() [1/6]

constexpr Rational operator+ ( const Rational a )

constexprnoexcept

Positive.

Parameters

[in] a Any Rational

Returns: constexpr Rational a

Definition at line 407 of file rational.h.

References a.

Referenced by operator+().

◆ operator+() [2/6]

constexpr Rational operator+	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Addition.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: constexpr Rational a + b

Definition at line 415 of file rational.h.

References a, and b.

◆ operator+() [3/6]

constexpr Rational operator+	(	const Rational	a,
		Index	b
	)

constexprnoexcept

Addition.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a + b

Definition at line 428 of file rational.h.

References a, and b.

◆ operator+() [4/6]

constexpr Rational operator+	(	const Rational	a,
		int	b
	)

constexprnoexcept

Addition.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a + b

Definition at line 438 of file rational.h.

References a, and b.

◆ operator+() [5/6]

constexpr Rational operator+	(	Index	b,
		const Rational	a
	)

constexprnoexcept

Addition.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational a + b

Definition at line 448 of file rational.h.

References a, b, and operator+().

◆ operator+() [6/6]

constexpr Rational operator+	(	int	b,
		const Rational	a
	)

constexprnoexcept

Addition.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational a + b

Definition at line 456 of file rational.h.

References a, b, and operator+().

◆ operator-() [1/6]

constexpr Rational operator- ( const Rational a )

constexprnoexcept

Negative.

Parameters

[in] a Any Rational

Returns: constexpr Rational Negative a

Definition at line 398 of file rational.h.

References a.

◆ operator-() [2/6]

constexpr Rational operator-	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Subtraction.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: constexpr Rational a - b

Definition at line 464 of file rational.h.

References a, and b.

◆ operator-() [3/6]

constexpr Rational operator-	(	const Rational	a,
		Index	b
	)

constexprnoexcept

Subtraction.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a - b

Definition at line 477 of file rational.h.

References a, and b.

◆ operator-() [4/6]

constexpr Rational operator-	(	const Rational	a,
		int	b
	)

constexprnoexcept

Subtraction.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a - b

Definition at line 487 of file rational.h.

References a, and b.

◆ operator-() [5/6]

constexpr Rational operator-	(	Index	b,
		const Rational	a
	)

constexprnoexcept

Subtraction.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational b - a

Definition at line 497 of file rational.h.

References a, and b.

◆ operator-() [6/6]

constexpr Rational operator-	(	int	b,
		const Rational	a
	)

constexprnoexcept

Subtraction.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational b - a

Definition at line 507 of file rational.h.

References a, and b.

◆ operator/() [1/5]

constexpr Rational operator/	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Division.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: constexpr Rational a / b

Definition at line 517 of file rational.h.

References a, and b.

◆ operator/() [2/5]

constexpr Rational operator/	(	const Rational	a,
		Index	b
	)

constexprnoexcept

Division.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a / b

Definition at line 527 of file rational.h.

References a, and b.

◆ operator/() [3/5]

constexpr Rational operator/	(	const Rational	a,
		int	b
	)

constexprnoexcept

Division.

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: constexpr Rational a / b

Definition at line 537 of file rational.h.

References a, and b.

◆ operator/() [4/5]

constexpr Rational operator/	(	Index	b,
		const Rational	a
	)

constexprnoexcept

Division.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational b / a

Definition at line 547 of file rational.h.

References a, and b.

◆ operator/() [5/5]

constexpr Rational operator/	(	int	b,
		const Rational	a
	)

constexprnoexcept

Division.

Parameters

[in]	b	Any Index
[in]	a	Any Rational

Returns: constexpr Rational b / a

Definition at line 557 of file rational.h.

References a, and b.

◆ operator<() [1/5]

constexpr bool operator<	(	const Index	a,
		const Rational	b
	)

constexprnoexcept

less

Parameters

[in]	a	Any Index
[in]	b	Any Rational

Returns: True if a is less than b

Definition at line 783 of file rational.h.

References a, and b.

◆ operator<() [2/5]

constexpr bool operator<	(	const int	a,
		const Rational	b
	)

constexprnoexcept

less

Parameters

[in]	a	Any Index
[in]	b	Any Rational

Returns: True if a is less than b

Definition at line 793 of file rational.h.

References a, and b.

◆ operator<() [3/5]

constexpr bool operator<	(	const Rational	a,
		const Index	b
	)

constexprnoexcept

less

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: True if a is less than b

Definition at line 803 of file rational.h.

References a, and b.

◆ operator<() [4/5]

constexpr bool operator<	(	const Rational	a,
		const int	b
	)

constexprnoexcept

less

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: True if a is less than b

Definition at line 813 of file rational.h.

References a, and b.

◆ operator<() [5/5]

constexpr bool operator<	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Less than.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: true If a < b; false Otherwise

Definition at line 690 of file rational.h.

References a, and b.

Referenced by operator>(), and operator>=().

◆ operator<<()

std::ostream & operator<<	(	std::ostream &	os,
		const Rational &	a
	)

Output operator.

Definition at line 33 of file rational.cc.

References a, Rational::Denom(), Rational::fixSign(), Rational::Nom(), and reduce_by_gcd().

◆ operator<=()

constexpr bool operator<=	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Less than or equal to.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: true If a <= b; false Otherwise

Definition at line 711 of file rational.h.

References a, b, and operator>().

◆ operator==() [1/3]

constexpr bool operator==	(	const Rational	a,
		const Index	b
	)

constexprnoexcept

equal

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: True if a is equal to b

Definition at line 863 of file rational.h.

References a, and b.

◆ operator==() [2/3]

constexpr bool operator==	(	const Rational	a,
		const int	b
	)

constexprnoexcept

equal

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: True if a is equal to b

Definition at line 873 of file rational.h.

References a, and b.

◆ operator==() [3/3]

constexpr bool operator==	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

Equality.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: true If equal; false Otherwise

Definition at line 667 of file rational.h.

References a, and b.

◆ operator>() [1/5]

constexpr bool operator>	(	const Index	a,
		const Rational	b
	)

constexprnoexcept

more

Parameters

[in]	a	Any Index
[in]	b	Any Rational

Returns: True if a is more than b

Definition at line 823 of file rational.h.

References a, and b.

◆ operator>() [2/5]

constexpr bool operator>	(	const int	a,
		const Rational	b
	)

constexprnoexcept

more

Parameters

[in]	a	Any Index
[in]	b	Any Rational

Returns: True if a is more than b

Definition at line 833 of file rational.h.

References a, and b.

◆ operator>() [3/5]

constexpr bool operator>	(	const Rational	a,
		const Index	b
	)

constexprnoexcept

more

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: True if a is more than b

Definition at line 843 of file rational.h.

References a, and b.

◆ operator>() [4/5]

constexpr bool operator>	(	const Rational	a,
		const int	b
	)

constexprnoexcept

more

Parameters

[in]	a	Any Rational
[in]	b	Any Index

Returns: True if a is more than b

Definition at line 853 of file rational.h.

References a, and b.

◆ operator>() [5/5]

constexpr bool operator>	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

More than.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: true If a > b; false Otherwise

Definition at line 702 of file rational.h.

References a, b, and operator<().

Referenced by operator<=().

◆ operator>=()

constexpr bool operator>=	(	const Rational	a,
		const Rational	b
	)

constexprnoexcept

More than or equal to.

Parameters

[in]	a	Any Rational
[in]	b	Any Rational

Returns: true If a >= b; false Otherwise

Definition at line 722 of file rational.h.

References a, b, and operator<().

◆ operator>>()

std::istream & operator>>	(	std::istream &	is,
		Rational &	a
	)

Input operator.

Definition at line 44 of file rational.cc.

References a, ARTS_USER_ERROR, ARTS_USER_ERROR_IF, my_basic_string< charT >::nelem(), Array< base >::nelem(), Absorption::nelem(), and my_basic_string< charT >::split().

◆ pow() [1/3]

Numeric pow	(	const Rational	base,
		const Rational	exp
	)

inline

Power of.

Parameters

[in]	base	Any Rational
[in]	exp	Any Rational

Returns: Numeric base to the power of exp

Definition at line 767 of file rational.h.

References pow(), and Rational::toNumeric().

◆ pow() [2/3]

Numeric pow	(	const Rational	base,
		Numeric	exp
	)

inline

Power of.

Parameters

[in]	base	Any Rational
[in]	exp	Any Numeric

Returns: Numeric base to the power of exp

Definition at line 747 of file rational.h.

References pow(), and Rational::toNumeric().

Referenced by abs_lookupSetup(), abs_lookupSetupBatch(), abs_lookupSetupWide(), antenna_responseGaussian(), antenna_responseVaryingGaussian(), BF86_CIA_N2(), cart2poslos(), CKD_mt_250_o2_vis(), CKD_mt_v1v0_o2(), lm_hitran_2017::compabs(), conti_n2__(), lm_hitran_2017::convtp(), CP98H2OAbsModel(), Minimize::T4::df(), Minimize::DPL::df(), diameter_maxFromDiameter_volume_equ(), diameter_volume_equFromDiameter_max(), doit_conv_flagLsq(), ELL07WaterDropletAbs(), TelsemAtlas::emis_interp(), fctl_(), g0Earth(), gaussian_response(), get_ppath_cloudvars(), Ho66_CO2_foreign_continuum(), Ho66_CO2_self_continuum(), binistream::ieee_double2float(), binistream::ieee_single2float(), iyIndependentBeamApproximation(), MaTipping_H2O_foreign_continuum(), matrix_exp(), mgd(), mgd_with_derivatives(), mod_gamma_dist(), MPM02H2OAbsModel(), MPM85O2AbsModel(), MPM87H2OAbsModel(), MPM87O2AbsModel(), MPM89H2OAbsModel(), MPM89O2AbsModel(), MPM92O2AbsModel(), MPM93_H2O_continuum(), MPM93_N2_continuum(), MPM93_O2_continuum(), MPM93H2OAbsModel(), MPM93IceCrystalAbs(), MPM93O2AbsModel(), MPM93RainExt(), MPM93WaterDropletAbs(), Minimize::T4::operator()(), Minimize::DPL::operator()(), Pardo_ATM_H2O_ForeignContinuum(), Pardo_ATM_N2_dry_continuum(), particle_bulkpropRadarOnionPeeling(), PFromZSimple(), polynomial_basis_func(), pow(), psd_cloudice_MH97(), psd_mgd_mass_and_something(), psd_rain_W16(), psdModifiedGammaMass(), PWR93O2AbsModel(), PWR98H2OAbsModel(), Absorption::ReadFromArtscat3Stream(), Absorption::ReadFromJplStream(), refellipsoidForAzimuth(), refellipsoidOrbitPlane(), Rosenkranz_CO2_foreign_continuum(), Rosenkranz_CO2_self_continuum(), Rosenkranz_N2_self_continuum(), Rosenkranz_O2_continuum(), rtmethods_jacobian_finalisation(), Legendre::schmidt(), Standard_H2O_foreign_continuum(), Standard_H2O_self_continuum(), Standard_N2_self_continuum(), Standard_O2_continuum(), surface_specular_R_and_b(), swv_mpmf87s93__(), transform_jacobian(), transform_x_back(), TRE05O2AbsModel(), yCalc(), and yRadar().

◆ pow() [3/3]

Numeric pow	(	Numeric	base,
		const Rational	exp
	)

inline

Power of.

Parameters

[in]	base	Any Numeric
[in]	exp	Any Rational

Returns: Numeric base to the power of exp

Definition at line 757 of file rational.h.

References pow(), and Rational::toNumeric().

◆ reduce_by_gcd()

constexpr Rational reduce_by_gcd ( const Rational a )

constexprnoexcept

Returns the rational reduced by the greates.

Parameters

[in] a Any Rational

Returns: a / gcd(a)

Definition at line 347 of file rational.h.

References a, and gcd().

Referenced by operator<<(), and Rational::simplify_in_place().

◆ sqrt()

Numeric sqrt ( const Rational r )

inline

Square root.

Parameters

[in] r Any Rational

Returns: Numeric Square root of the Rational

Definition at line 739 of file rational.h.

References sqrt(), and Rational::toNumeric().

Referenced by antenna_responseGaussian(), antenna_responseVaryingGaussian(), LineShape::SpeedDependentVoigt::calc(), cart2pol(), cart2poslos(), cart2sph(), cart2sph_plain(), cart2zaaa(), case_b_g_coefficient_o2(), cayley_hamilton_fitted_method_4x4_propmat_to_transmat__eigen(), cayley_hamilton_fitted_method_4x4_propmat_to_transmat__explicit(), lm_hitran_2017::compabs(), complex_n_ice_matzler06(), complex_n_water_liebe93(), compute_transmission_matrix(), compute_transmission_matrix_and_derivative(), compute_transmission_matrix_from_averaged_matrix_at_frequency(), lm_hitran_2017::convtp(), covmat_sxExtractSqrtDiagonal(), doit_conv_flagLsq(), Absorption::Lines::DopplerConstant(), dotprod_with_los(), MCAntenna::draw_los(), dtransmat3(), Absorption::LineMixing::Makarov2020etal::erot(), Zeeman::FromGrids(), gaussian_response(), gaussian_response_autogrid(), geompath_l_at_r(), geompath_r_at_l(), geompath_tanpos_3d(), Absorption::PredefinedModel::makarov2020_o2_lines_mpm(), MCGeneral(), LineShape::HartmannTran::operator()(), Absorption::LineMixing::PopulationAndDipole::PopulationAndDipole(), psd_cloudice_MH97(), r_crossing_3d(), ran_gaussian(), TelsemAtlas::read(), lm_hitran_2017::readlines(), Absorption::LineMixing::Makarov2020etal::reduced_dipole(), Absorption::reduced_magnetic_quadrapole(), refellipsoidForAzimuth(), refellipsoidOrbitPlane(), refr_index_airInfraredEarth(), relaxation_matrix_element(), Absorption::LineMixing::Makarov2020etal::relaxation_matrix_offdiagonal(), retrievalErrorsExtract(), Legendre::schmidt(), sphdist(), sqrt(), surf_radius_at_l(), test2(), transmat3(), unitl(), vector_angle(), and yCalc().

Classes

Macros

Typedefs

Functions

Detailed Description

Macro Definition Documentation

◆ RATIONAL_UNDEFINED

Typedef Documentation

◆ ArrayOfRational

Function Documentation

◆ abs()

◆ gcd()

◆ iseven()

◆ max()

◆ min()

◆ numeric2rational()

◆ operator!()

◆ operator!=() [1/3]

◆ operator!=() [2/3]

◆ operator!=() [3/3]

◆ operator""_2()

◆ operator%() [1/5]

◆ operator%() [2/5]

◆ operator%() [3/5]

◆ operator%() [4/5]

◆ operator%() [5/5]

◆ operator*() [1/5]

◆ operator*() [2/5]

◆ operator*() [3/5]

◆ operator*() [4/5]

◆ operator*() [5/5]

◆ operator+() [1/6]

◆ operator+() [2/6]

◆ operator+() [3/6]

◆ operator+() [4/6]

◆ operator+() [5/6]

◆ operator+() [6/6]

◆ operator-() [1/6]

◆ operator-() [2/6]

◆ operator-() [3/6]

◆ operator-() [4/6]

◆ operator-() [5/6]

◆ operator-() [6/6]

◆ operator/() [1/5]

◆ operator/() [2/5]

◆ operator/() [3/5]

◆ operator/() [4/5]

◆ operator/() [5/5]

◆ operator<() [1/5]

◆ operator<() [2/5]

◆ operator<() [3/5]

◆ operator<() [4/5]

◆ operator<() [5/5]

◆ operator<<()

◆ operator<=()

◆ operator==() [1/3]

◆ operator==() [2/3]

◆ operator==() [3/3]

◆ operator>() [1/5]

◆ operator>() [2/5]

◆ operator>() [3/5]

◆ operator>() [4/5]

◆ operator>() [5/5]

◆ operator>=()

◆ operator>>()

◆ pow() [1/3]

◆ pow() [2/3]

◆ pow() [3/3]

◆ reduce_by_gcd()

◆ sqrt()