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 <ostream>

Go to the source code of this file.

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 (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...
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 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(), Absorption::reduced_magnetic_quadrapole(), 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 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.

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 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*() [1/7]

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 567 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 577 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 587 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 597 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 605 of file rational.h.

References a, b, and operator*().

operator*() [6/7]

constexpr Numeric operator* ( Numeric  x, Rational  y  )

constexprnoexcept

Definition at line 948 of file rational.h.

References Rational::toNumeric().

operator*() [7/7]

constexpr Numeric operator* ( Rational  y, Numeric  x  )

constexprnoexcept

Multiplication with numeric.

Definition at line 947 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 407 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 415 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 428 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 438 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 448 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 456 of file rational.h.

References a, b, and operator+().

operator+() [7/8]

constexpr Numeric operator+ ( Numeric  x, Rational  y  )

constexprnoexcept

Definition at line 956 of file rational.h.

References Rational::toNumeric().

operator+() [8/8]

constexpr Numeric operator+ ( Rational  y, Numeric  x  )

constexprnoexcept

Addition with numeric.

Definition at line 955 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 398 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 464 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 477 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 487 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 497 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 507 of file rational.h.

References a, and b.

operator-() [7/8]

constexpr Numeric operator- ( Numeric  x, Rational  y  )

constexprnoexcept

Definition at line 960 of file rational.h.

References Rational::toNumeric().

operator-() [8/8]

constexpr Numeric operator- ( Rational  y, Numeric  x  )

constexprnoexcept

Subtraction with numeric.

Definition at line 959 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 517 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 527 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 537 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 547 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 557 of file rational.h.

References a, and b.

operator/() [6/7]

constexpr Numeric operator/ ( Numeric  x, Rational  y  )

constexprnoexcept

Definition at line 952 of file rational.h.

References Rational::toNumeric().

operator/() [7/7]

constexpr Numeric operator/ ( Rational  y, Numeric  x  )

constexprnoexcept

Division with numeric.

Definition at line 951 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 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 34 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.

Referenced by Species::ENUMCLASS().

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 45 of file rational.cc.

References a, and ARTS_USER_ERROR_IF.

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(), 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(), 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 ( 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<<(), 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 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(), IntersectionGeometricalWithAltitude(), 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(), Absorption::LineMixing::LinearRovibErrorCorrectedSudden::relaxation_matrix_offdiagonal(), retrievalErrorsExtract(), Legendre::schmidt(), sphdist(), sqrt(), surf_radius_at_l(), test2(), transmat3(), unitl(), vector_angle(), and yCalc().