rational.h File Reference

Contains the rational class definition. More...

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

Go to the source code of this file.

Classes
struct	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 Rational	reduce_by_gcd (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...
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...
constexpr Numeric	operator* (Rational y, Numeric x) noexcept
	Multiplication with numeric. More...
constexpr Numeric	operator* (Numeric x, Rational y) noexcept
constexpr Numeric	operator/ (Rational y, Numeric x) noexcept
	Division with numeric. More...
constexpr Numeric	operator/ (Numeric x, Rational y) noexcept
constexpr Numeric	operator+ (Rational y, Numeric x) noexcept
	Addition with numeric. More...
constexpr Numeric	operator+ (Numeric x, Rational y) noexcept
constexpr Numeric	operator- (Rational y, Numeric x) noexcept
	Subtraction with numeric. More...
constexpr Numeric	operator- (Numeric x, Rational y) noexcept

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 357 of file rational.h.

Typedef Documentation

ArrayOfRational

using ArrayOfRational = Array<Rational>

Definition at line 886 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 862 of file rational.h.

References a.

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 902 of file rational.h.

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

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 872 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 882 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 329 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.numer and a.isDefined()

false Otherwise

Definition at line 698 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 843 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 853 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 645 of file rational.h.

References a, and b.

Referenced by Species::ENUMCLASS().

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 893 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 579 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 592 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 602 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 612 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 622 of file rational.h.

References a, and b.

operator*() [1/7]

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 533 of file rational.h.

References a, and b.

Referenced by operator*().

operator*() [2/7]

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 543 of file rational.h.

References a, and b.

operator*() [3/7]

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 553 of file rational.h.

References a, and b.

operator*() [4/7]

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 563 of file rational.h.

References a, b, and operator*().

operator*() [5/7]

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 571 of file rational.h.

References a, b, and operator*().

operator*() [6/7]

constexpr Numeric operator* ( Numeric  x, Rational  y  )

constexprnoexcept

Definition at line 908 of file rational.h.

References Rational::toNumeric().

operator*() [7/7]

constexpr Numeric operator* ( Rational  y, Numeric  x  )

constexprnoexcept

Multiplication with numeric.

Definition at line 907 of file rational.h.

References Rational::toNumeric().

operator+() [1/8]

constexpr Rational operator+ ( const Rational  a )

constexprnoexcept

Positive.

Parameters

[in]

a

Any Rational

Returns

constexpr Rational a

Definition at line 373 of file rational.h.

References a.

Referenced by operator+().

operator+() [2/8]

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 381 of file rational.h.

References a, and b.

operator+() [3/8]

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 394 of file rational.h.

References a, and b.

operator+() [4/8]

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 404 of file rational.h.

References a, and b.

operator+() [5/8]

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 414 of file rational.h.

References a, b, and operator+().

operator+() [6/8]

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 422 of file rational.h.

References a, b, and operator+().

operator+() [7/8]

constexpr Numeric operator+ ( Numeric  x, Rational  y  )

constexprnoexcept

Definition at line 916 of file rational.h.

References Rational::toNumeric().

operator+() [8/8]

constexpr Numeric operator+ ( Rational  y, Numeric  x  )

constexprnoexcept

Addition with numeric.

Definition at line 915 of file rational.h.

References Rational::toNumeric().

operator-() [1/8]

constexpr Rational operator- ( const Rational  a )

constexprnoexcept

Negative.

Parameters

[in]

a

Any Rational

Returns

constexpr Rational Negative a

Definition at line 364 of file rational.h.

References a.

operator-() [2/8]

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 430 of file rational.h.

References a, and b.

operator-() [3/8]

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 443 of file rational.h.

References a, and b.

operator-() [4/8]

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 453 of file rational.h.

References a, and b.

operator-() [5/8]

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 463 of file rational.h.

References a, and b.

operator-() [6/8]

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 473 of file rational.h.

References a, and b.

operator-() [7/8]

constexpr Numeric operator- ( Numeric  x, Rational  y  )

constexprnoexcept

Definition at line 920 of file rational.h.

References Rational::toNumeric().

operator-() [8/8]

constexpr Numeric operator- ( Rational  y, Numeric  x  )

constexprnoexcept

Subtraction with numeric.

Definition at line 919 of file rational.h.

References Rational::toNumeric().

operator/() [1/7]

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 483 of file rational.h.

References a, and b.

operator/() [2/7]

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 493 of file rational.h.

References a, and b.

operator/() [3/7]

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 503 of file rational.h.

References a, and b.

operator/() [4/7]

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 513 of file rational.h.

References a, and b.

operator/() [5/7]

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 523 of file rational.h.

References a, and b.

operator/() [6/7]

constexpr Numeric operator/ ( Numeric  x, Rational  y  )

constexprnoexcept

Definition at line 912 of file rational.h.

References Rational::toNumeric().

operator/() [7/7]

constexpr Numeric operator/ ( Rational  y, Numeric  x  )

constexprnoexcept

Division with numeric.

Definition at line 911 of file rational.h.

References Rational::toNumeric().

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 743 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 753 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 763 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 773 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 656 of file rational.h.

References a, and b.

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

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 677 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 823 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 833 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 633 of file rational.h.

References a, and b.

Referenced by Species::ENUMCLASS(), and Quantum::Number::Value::good().

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 783 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 793 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 803 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 813 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 668 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 688 of file rational.h.

References a, b, and operator<().

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 733 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 713 of file rational.h.

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

Referenced by antenna_responseGaussian(), antenna_responseVaryingGaussian(), BF86_CIA_N2(), bound32_(), bound54_(), cart2poslos(), CKD_222_self_h2o(), CKD_242_self_h2o(), CKD_mt_100_self_h2o(), CKD_mt_250_CIAfun_n2(), CKD_mt_250_CIArot_n2(), CKD_mt_250_co2(), CKD_mt_250_foreign_h2o(), CKD_mt_250_o2_vis(), CKD_mt_250_self_h2o(), CKD_mt_320_foreign_h2o(), CKD_mt_320_self_h2o(), CKD_mt_CIArot_n2(), CKD_mt_v1v0_o2(), lm_hitran_2017::compabs(), conti_n2__(), lm_hitran_2017::convtp(), CP98H2OAbsModel(), delanoe_shape_with_derivative(), Minimize::T4::df(), Minimize::DPL::df(), diameter_maxFromDiameter_volume_equ(), diameter_volume_equFromDiameter_max(), dm_from_iwc_n0(), doit_conv_flagLsq(), ELL07WaterDropletAbs(), TelsemAtlas::emis_interp(), fctl_(), g0Earth(), gaussian_response(), get_ppath_cloudvars(), Ho66_CO2_foreign_continuum(), Ho66_CO2_self_continuum(), IntersectionGeometricalWithAltitude(), 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(), n0_from_iwc_dm(), 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_mgd_smm_common(), psd_MY05(), psd_rain_W16(), psd_SB06(), psd_snow_F07(), 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(), Legendre::schmidt_fieldcalc(), Standard_H2O_foreign_continuum(), Standard_H2O_self_continuum(), Standard_N2_self_continuum(), Standard_O2_continuum(), surface_specular_R_and_b(), surfaceMapToLinearPolarisation(), swv24_(), swv_mpmf87s93__(), test01(), 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 723 of file rational.h.

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

reduce_by_gcd()

constexpr Rational reduce_by_gcd ( Rational  a )

constexprnoexcept

Returns the rational reduced by the greates.

Parameters

[in]

a

Any Rational

Returns

a / gcd(a)

Definition at line 315 of file rational.h.

References a.

Referenced by Rational::simplify_in_place(), Quantum::Number::Value::Value(), and Quantum::Number::value_holder().

sqrt()

Numeric sqrt ( const Rational  r )

inline

Square root.

Parameters

[in]

r

Any Rational

Returns

Numeric Square root of the Rational

Definition at line 705 of file rational.h.

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

Referenced by antenna_responseGaussian(), antenna_responseVaryingGaussian(), bgama_(), LineShape::SpeedDependentVoigt::calc(), LineShape::HartmannTran::calc(), cart2geodetic(), cart2pol(), cart2poslos(), cart2sph(), cart2sph_plain(), cart2zaaa(), case_b_g_coefficient_o2(), 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(), dwigner3j(), Absorption::LineMixing::Makarov2020etal::erot(), Zeeman::FromGrids(), gaussian_response(), gaussian_response_autogrid(), geodetic2cart(), geodeticposlos2cart(), geompath_l_at_r(), geompath_r_at_l(), geompath_tanpos_3d(), get_star_radiation(), lm_hitran_2017::hitran_lm_eigenvalue_approximation(), LineShape::SpeedDependentVoigt::init(), LineShape::HartmannTran::init(), IntersectionGeometricalWithAltitude(), line_circle_intersect(), line_refellipsoid_intersect(), line_sphere_intersect(), MCGeneral(), MCRadar(), LineShape::HartmannTran::operator()(), Absorption::LineMixing::PopulationAndDipole::PopulationAndDipole(), ppathFixedLstep(), psd_cloudice_MH97(), r_crossing_3d(), IGRF::radius(), ran_gaussian(), TelsemAtlas::read(), lm_hitran_2017::readlines(), Absorption::LineMixing::Makarov2020etal::reduced_dipole(), Absorption::reduced_magnetic_quadrapole(), Absorption::reduced_rovibrational_dipole(), refell2r(), refellipsoidForAzimuth(), refellipsoidOrbitPlane(), refr_index_airFreeElectrons(), refr_index_airInfraredEarth(), refractive_index_water_and_steam_VisNIR(), relaxation_matrix_element(), Absorption::LineMixing::Makarov2020etal::relaxation_matrix_offdiagonal(), Absorption::LineMixing::LinearRovibErrorCorrectedSudden::relaxation_matrix_offdiagonal(), retrievalErrorsExtract(), rotationmat3D(), Legendre::schmidt(), sphdist(), sqrt(), surf_radius_at_l(), test2(), test31(), test_oem_gauss_newton(), test_oem_levenberg_marquardt(), test_oem_linear(), Legendre::to_geodetic(), transmat3(), unitl(), vector_angle(), and yCalc().