rational.h File Reference

Contains the rational class definition. More...

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

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
typedef Array< Rational >	ArrayOfRational

Functions
constexpr Index	gcd (Index a, Index b)
	Returns the greatest common denominator of two numbers. More...
constexpr Rational	reduce_by_gcd (const Rational a)
	Returns the rational reduced by the greates. More...
constexpr Rational	numeric2rational (Numeric x, size_t maxdec=4)
	Rational from Numeric. More...
constexpr Rational	operator- (const Rational a)
	Negative. More...
constexpr Rational	operator+ (const Rational a)
	Positive. More...
constexpr Rational	operator+ (const Rational a, const Rational b)
	Addition. More...
constexpr Rational	operator+ (const Rational a, Index b)
	Addition. More...
constexpr Rational	operator+ (Index b, const Rational a)
	Addition. More...
constexpr Rational	operator- (const Rational a, const Rational b)
	Subtraction. More...
constexpr Rational	operator- (const Rational a, Index b)
	Subtraction. More...
constexpr Rational	operator- (Index b, const Rational a)
	Subtraction. More...
constexpr Rational	operator/ (const Rational a, const Rational b)
	Division. More...
constexpr Rational	operator/ (const Rational a, Index b)
	Division. More...
constexpr Rational	operator/ (Index b, const Rational a)
	Division. More...
constexpr Rational	operator* (const Rational a, const Rational b)
	Multiplication. More...
constexpr Rational	operator* (const Rational a, Index b)
	Multiplication. More...
constexpr Rational	operator* (Index b, const Rational a)
	Multiplication. More...
constexpr Rational	operator% (const Rational a, const Rational b)
	Remainder. More...
constexpr Rational	operator% (const Rational a, Index b)
	Remainder. More...
constexpr Rational	operator% (Index b, const Rational a)
	Remainder. More...
constexpr bool	operator== (const Rational a, const Rational b)
	Equality. More...
constexpr bool	operator!= (Rational a, Rational b)
	Inequality. More...
constexpr bool	operator< (Rational a, Rational b)
	Less than. More...
constexpr bool	operator> (Rational a, Rational b)
	More than. More...
constexpr bool	operator<= (Rational a, Rational b)
	Less than or equal to. More...
constexpr bool	operator>= (const Rational a, const Rational b)
	More than or equal to. More...
constexpr bool	operator! (const Rational a)
	Not. More...
Numeric	fac (const Rational r)
	Factorial. 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)
	less More...
constexpr bool	operator< (const Rational a, const Index b)
	less More...
constexpr bool	operator> (const Index a, const Rational b)
	more More...
constexpr bool	operator> (const Rational a, const Index b)
	more More...
constexpr bool	operator== (const Rational a, const Index b)
	equal More...
constexpr bool	operator!= (const Rational a, const Index b)
	not equal More...
constexpr Rational	abs (const Rational a)
	Absolute. More...
constexpr Rational	max (const Rational a, const Rational b)
	Maximum. More...
constexpr Rational	operator""_2 (unsigned long long int n)
	Returns common operator n/2. More...
constexpr Rational	operator""_rat (unsigned long long int n)
	Returns common operator n/1. More...
constexpr bool	even (const Rational r)
	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 361 of file rational.h.

Typedef Documentation

ArrayOfRational

typedef Array<Rational> ArrayOfRational

Definition at line 737 of file rational.h.

Function Documentation

abs()

constexpr Rational abs ( const Rational  a )

constexpr

Absolute.

Parameters

[in]

a

Any Rational

Returns

constexpr Rational Absolute value of the Rational

Definition at line 723 of file rational.h.

even()

constexpr bool even ( const Rational  r )

constexpr

Returns true if even integer.

Parameters

[in]

r

Any rational

Returns

true if r is even, otherwise false

Definition at line 762 of file rational.h.

Referenced by o2_ecs_wigner_symbol_tran(), o2_makarov2013_reduced_dipole(), and Absorption::reduced_magnetic_quadrapole().

fac()

Numeric fac ( const Rational  r )

inline

Factorial.

Parameters

[in]

r

Any Rational

Returns

Numeric Factorial of the Rational

Definition at line 613 of file rational.h.

References Rational::toIndex().

gcd()

constexpr Index gcd ( Index  a, Index  b  )

constexpr

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 45 of file rational.h.

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

max()

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

constexpr

Maximum.

Parameters

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

Returns

constexpr Rational Largest of a and b

Definition at line 733 of file rational.h.

numeric2rational()

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

constexpr

Rational from Numeric.

Performs basic rounding

Parameters

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

Definition at line 330 of file rational.h.

References ARTS::Var::x().

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

operator!()

constexpr bool operator! ( const Rational  a )

constexpr

Not.

Parameters

[in]

a

Any Rational

Returns

true If a.Nom() and a.isDefined()

false Otherwise

Definition at line 606 of file rational.h.

References Rational::isDefined(), and Rational::Nom().

operator!=() [1/2]

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

constexpr

not equal

Parameters

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

Returns

True if a is not equal to b

Definition at line 714 of file rational.h.

operator!=() [2/2]

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

constexpr

Inequality.

Parameters

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

Returns

true If not equal

false Otherwise

Definition at line 553 of file rational.h.

References operator==().

operator""_2()

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

constexpr

Returns common operator n/2.

Parameters

[in]

n

Any positive integer

Returns

Rational(n, 2)

Definition at line 744 of file rational.h.

operator""_rat()

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

constexpr

Returns common operator n/1.

Parameters

[in]

n

Any positive integer

Returns

Rational(n, 1)

Definition at line 753 of file rational.h.

operator%() [1/3]

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

constexpr

Remainder.

Parameters

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

Returns

constexpr Rational a % b

Definition at line 507 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator%() [2/3]

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

constexpr

Remainder.

Parameters

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

Returns

constexpr Rational a % b

Definition at line 520 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator%() [3/3]

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

constexpr

Remainder.

Parameters

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

Returns

constexpr Rational b % a

Definition at line 530 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator*() [1/3]

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

constexpr

Multiplication.

Parameters

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

Returns

constexpr Rational a * b

Definition at line 479 of file rational.h.

References Rational::Denom(), and Rational::Nom().

Referenced by operator*().

operator*() [2/3]

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

constexpr

Multiplication.

Parameters

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

Returns

constexpr Rational a * b

Definition at line 489 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator*() [3/3]

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

constexpr

Multiplication.

Parameters

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

Returns

constexpr Rational a * b

Definition at line 499 of file rational.h.

References operator*().

operator+() [1/4]

constexpr Rational operator+ ( const Rational  a )

constexpr

Positive.

Parameters

[in]

a

Any Rational

Returns

constexpr Rational a

Definition at line 377 of file rational.h.

Referenced by operator+().

operator+() [2/4]

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

constexpr

Addition.

Parameters

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

Returns

constexpr Rational a + b

Definition at line 385 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator+() [3/4]

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

constexpr

Addition.

Parameters

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

Returns

constexpr Rational a + b

Definition at line 398 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator+() [4/4]

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

constexpr

Addition.

Parameters

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

Returns

constexpr Rational a + b

Definition at line 408 of file rational.h.

References operator+().

operator-() [1/4]

constexpr Rational operator- ( const Rational  a )

constexpr

Negative.

Parameters

[in]

a

Any Rational

Returns

constexpr Rational Negative a

Definition at line 368 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator-() [2/4]

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

constexpr

Subtraction.

Parameters

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

Returns

constexpr Rational a - b

Definition at line 416 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator-() [3/4]

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

constexpr

Subtraction.

Parameters

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

Returns

constexpr Rational a - b

Definition at line 429 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator-() [4/4]

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

constexpr

Subtraction.

Parameters

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

Returns

constexpr Rational b - a

Definition at line 439 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator/() [1/3]

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

constexpr

Division.

Parameters

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

Returns

constexpr Rational a / b

Definition at line 449 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator/() [2/3]

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

constexpr

Division.

Parameters

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

Returns

constexpr Rational a / b

Definition at line 459 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator/() [3/3]

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

constexpr

Division.

Parameters

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

Returns

constexpr Rational b / a

Definition at line 469 of file rational.h.

References Rational::Denom(), and Rational::Nom().

operator<() [1/3]

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

constexpr

less

Parameters

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

Returns

True if a is less than b

Definition at line 664 of file rational.h.

operator<() [2/3]

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

constexpr

less

Parameters

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

Returns

True if a is less than b

Definition at line 674 of file rational.h.

operator<() [3/3]

constexpr bool operator< ( Rational  a, Rational  b  )

constexpr

Less than.

Parameters

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

Returns

true If a < b

false Otherwise

Definition at line 564 of file rational.h.

References Rational::Denom(), Rational::isDefined(), and Rational::Nom().

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

operator<=()

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

constexpr

Less than or equal to.

Parameters

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

Returns

true If a <= b

false Otherwise

Definition at line 585 of file rational.h.

References operator>().

operator==() [1/2]

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

constexpr

equal

Parameters

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

Returns

True if a is equal to b

Definition at line 704 of file rational.h.

operator==() [2/2]

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

constexpr

Equality.

Parameters

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

Returns

true If equal

false Otherwise

Definition at line 541 of file rational.h.

References Rational::Denom(), Rational::isDefined(), and Rational::Nom().

Referenced by operator!=().

operator>() [1/3]

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

constexpr

more

Parameters

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

Returns

True if a is more than b

Definition at line 684 of file rational.h.

operator>() [2/3]

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

constexpr

more

Parameters

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

Returns

True if a is more than b

Definition at line 694 of file rational.h.

operator>() [3/3]

constexpr bool operator> ( Rational  a, Rational  b  )

constexpr

More than.

Parameters

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

Returns

true If a > b

false Otherwise

Definition at line 576 of file rational.h.

References operator<().

Referenced by operator<=().

operator>=()

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

constexpr

More than or equal to.

Parameters

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

Returns

true If a >= b

false Otherwise

Definition at line 596 of file rational.h.

References operator<().

operator>>()

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

Input operator.

Definition at line 44 of file rational.cc.

References Array< base >::nelem(), and Absorption::nelem().

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 648 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 628 of file rational.h.

References 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(), conti_n2__(), CP98H2OAbsModel(), 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(), 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(), o2_ecs_ql_makarov(), p_gridRefine(), Pardo_ATM_H2O_ForeignContinuum(), Pardo_ATM_N2_dry_continuum(), PFromZSimple(), polynomial_basis_func(), pow(), psd_cloudice_MH97(), psd_mgd_mass_and_something(), psd_rain_W16(), psdModifiedGammaMass(), PWR93O2AbsModel(), PWR98H2OAbsModel(), refellipsoidForAzimuth(), refellipsoidOrbitPlane(), Rosenkranz_CO2_foreign_continuum(), Rosenkranz_CO2_self_continuum(), Rosenkranz_N2_self_continuum(), Rosenkranz_O2_continuum(), rtmethods_jacobian_finalisation(), Standard_H2O_foreign_continuum(), Standard_H2O_self_continuum(), Standard_N2_self_continuum(), Standard_O2_continuum(), surface_specular_R_and_b(), swv_mpmf87s93__(), test07(), transform_x_back(), TRE05O2AbsModel(), yActive(), and yCalc().

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 638 of file rational.h.

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

reduce_by_gcd()

constexpr Rational reduce_by_gcd ( const Rational  a )

constexpr

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 Rational::Denom(), gcd(), and Rational::Nom().

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 620 of file rational.h.

References Rational::toNumeric().

Referenced by abs_lookupTestAccMC(), antenna_responseGaussian(), antenna_responseVaryingGaussian(), cart2pol(), cart2poslos(), cart2sph(), cart2zaaa(), case_b_g_coefficient_o2(), cayley_hamilton_fitted_method_4x4_propmat_to_transmat__eigen(), cayley_hamilton_fitted_method_4x4_propmat_to_transmat__explicit(), chk_atm_vecfield_lat90(), complex_n_ice_matzler06(), complex_n_water_liebe93(), compute_transmission_matrix_from_averaged_matrix_at_frequency(), covmat_sxExtractSqrtDiagonal(), distance2D(), distance3D(), doit_conv_flagLsq(), Linefunctions::DopplerConstant(), dotprod_with_los(), MCAntenna::draw_los(), Zeeman::FromGrids(), g_legendre_poly(), g_legendre_poly_deriv(), g_legendre_poly_norm_schmidt(), g_legendre_poly_norm_schmidt_deriv(), g_legendre_poly_norm_schmidt_deriv1(), g_legendre_poly_norm_schmidt_deriv2(), g_legendre_poly_norm_schmidt_deriv3(), g_legendre_poly_norm_schmidt_deriv4(), gaussian_response(), gaussian_response_autogrid(), geompath_l_at_r(), geompath_r_at_l(), geompath_tanpos_3d(), legendre_poly(), legendre_poly_deriv(), legendre_poly_norm_schmidt(), legendre_poly_norm_schmidt_deriv(), los2xyz(), MCGeneral(), o2_ecs_wigner_symbol_tran(), o2_makarov2013_reduced_dipole(), psd_cloudice_MH97(), r_crossing_3d(), ran_gaussian(), TelsemAtlas::read(), Absorption::reduced_magnetic_quadrapole(), refellipsoidForAzimuth(), refellipsoidOrbitPlane(), refr_index_airInfraredEarth(), retrievalErrorsExtract(), Linefunctions::set_htp(), sphdist(), test2(), unitl(), vector_angle(), and yCalc().