High-precision rational numbers. More...

#include <vnl_rational.h>

Public Member Functions
	vnl_rational ()
	Creates a rational with given numerator and denominator. More...

	vnl_rational (long num)

	vnl_rational (long num, long den)

	vnl_rational (unsigned long num)

	vnl_rational (unsigned long num, unsigned long den)

	vnl_rational (int num)

	vnl_rational (int num, int den)

	vnl_rational (unsigned int num)

	vnl_rational (unsigned int num, unsigned int den)

	vnl_rational (short num)

	vnl_rational (short num, short den)

	vnl_rational (unsigned short num)

	vnl_rational (unsigned short num, unsigned short den)

	vnl_rational (double d)
	Creates a rational from a double. More...

	vnl_rational (float d)
	Creates a rational from a double. More...

	vnl_rational (vnl_rational const &from)

	~vnl_rational ()=default

void	set (long num, long den)

long	numerator () const
	Return the numerator of the (simplified) rational number representation. More...

long	denominator () const
	Return the denominator of the (simplified) rational number representation. More...

vnl_rational &	operator= (vnl_rational const &rhs)
	Copies the contents and state of rhs rational over to the lhs. More...

bool	operator== (vnl_rational const &rhs) const
	Returns true if the two rationals have the same representation. More...

bool	operator!= (vnl_rational const &rhs) const

bool	operator== (long rhs) const

bool	operator!= (long rhs) const

bool	operator== (int rhs) const

bool	operator!= (int rhs) const

vnl_rational	operator- () const
	Unary minus - returns the negation of the current rational. More...

vnl_rational	operator+ () const
	Unary plus - returns the current rational. More...

bool	operator! () const
	Unary not - returns true if rational is equal to zero. More...

vnl_rational	abs () const
	Returns the absolute value of the current rational. More...

vnl_rational &	invert ()
	Replaces rational with 1/rational and returns it. More...

vnl_rational &	operator+= (vnl_rational const &r)
	Plus/assign: replace lhs by lhs + rhs. More...

vnl_rational &	operator+= (long r)

vnl_rational &	operator-= (vnl_rational const &r)
	Minus/assign: replace lhs by lhs - rhs. More...

vnl_rational &	operator-= (long r)

vnl_rational &	operator *= (vnl_rational const &r)
	Multiply/assign: replace lhs by lhs * rhs. More...

vnl_rational &	operator *= (long r)
	Multiply/assign: replace lhs by lhs * rhs. More...

vnl_rational &	operator/= (vnl_rational const &r)
	Divide/assign: replace lhs by lhs / rhs. More...

vnl_rational &	operator/= (long r)
	Divide/assign: replace lhs by lhs / rhs. More...

vnl_rational &	operator%= (vnl_rational const &r)
	Modulus/assign: replace lhs by lhs % rhs. More...

vnl_rational &	operator%= (long r)

vnl_rational &	operator++ ()
	Pre-increment (++r). No-op when +-Inf. More...

vnl_rational &	operator-- ()
	Pre-decrement (–r). No-op when +-Inf. More...

vnl_rational	operator++ (int)
	Post-increment (r++). No-op when +-Inf. More...

vnl_rational	operator-- (int)
	Post-decrement (r–). No-op when +-Inf. More...

bool	operator< (vnl_rational const &rhs) const

bool	operator> (vnl_rational const &r) const

bool	operator<= (vnl_rational const &r) const

bool	operator>= (vnl_rational const &r) const

bool	operator< (long r) const

bool	operator> (long r) const

bool	operator<= (long r) const

bool	operator>= (long r) const

bool	operator< (int r) const

bool	operator> (int r) const

bool	operator<= (int r) const

bool	operator>= (int r) const

bool	operator< (double r) const

bool	operator> (double r) const

bool	operator<= (double r) const

bool	operator>= (double r) const

long	truncate () const
	Converts rational value to integer by truncating towards zero. More...

long	floor () const
	Converts rational value to integer by truncating towards negative infinity. More...

long	ceil () const
	Converts rational value to integer by truncating towards positive infinity. More...

long	round () const
	Rounds rational to nearest integer. More...

	operator short ()

	operator int ()

	operator long () const

	operator long ()

	operator float () const

	operator float ()

	operator double () const

	operator double ()

Static Public Member Functions
static long	gcd (long l1, long l2)
	Calculate greatest common divisor of two integers. More...

Private Member Functions
void	normalize ()
	Private function to normalize numerator/denominator of rational number. More...

Private Attributes
long	num_
	Numerator portion. More...

long	den_
	Denominator portion. More...

Related Functions
(Note that these are not member functions.)
void	vsl_b_write (vsl_b_ostream &os, vnl_rational const &v)
	Binary save vnl_rational to stream. More...

void	vsl_b_read (vsl_b_istream &is, vnl_rational &v)
	Binary load vnl_rational from stream. More...

void	vsl_print_summary (std::ostream &os, vnl_rational const &b)
	Print human readable summary of object to a stream. More...

std::ostream &	operator<< (std::ostream &s, vnl_rational const &r)
	formatted output. More...

std::istream &	operator>> (std::istream &s, vnl_rational &r)
	simple input. More...

vnl_rational	operator+ (vnl_rational const &r1, vnl_rational const &r2)
	Returns the sum of two rational numbers. More...

vnl_rational	operator- (vnl_rational const &r1, vnl_rational const &r2)
	Returns the difference of two rational numbers. More...

vnl_rational	operator * (vnl_rational const &r1, vnl_rational const &r2)
	Returns the product of two rational numbers. More...

vnl_rational	operator/ (vnl_rational const &r1, vnl_rational const &r2)
	Returns the quotient of two rational numbers. More...

vnl_rational	operator% (vnl_rational const &r1, vnl_rational const &r2)
	Returns the remainder of r1 divided by r2. More...

Detailed Description

High-precision rational numbers.

The vnl_rational class provides high-precision rational numbers and arithmetic, using the built-in type long, for the numerator and denominator. Implicit conversion to the system defined types short, int, long, float, and double is supported by overloaded operator member functions. Although the rational class makes judicious use of inline functions and deals only with integral values, the user is warned that the rational integer arithmetic class is still considerably slower than the built-in integer data types. If the range of values anticipated will fit into a built-in type, use that instead.

In addition to the original COOL Rational class, vnl_rational is able to represent plus and minus infinity. An other interesting addition is the possibility to construct a rational from a double. This allows for lossless conversion from e.g. double 1.0/3.0 to the rational number 1/3, hence no more rounding errors. This is implemented with continued fraction approximations.

Definition at line 73 of file vnl_rational.h.

Constructor & Destructor Documentation

◆ vnl_rational() [1/16]

vnl_rational::vnl_rational ( )

inline

Creates a rational with given numerator and denominator.

Default constructor gives 0. Also serves as automatic cast from long to vnl_rational. The only input which is not allowed is (0,0); the denominator is allowed to be 0, to represent +Inf or -Inf.

Definition at line 86 of file vnl_rational.h.

◆ vnl_rational() [2/16]

vnl_rational::vnl_rational ( long num )

inline

Definition at line 89 of file vnl_rational.h.

◆ vnl_rational() [3/16]

vnl_rational::vnl_rational	(	long	num,
		long	den
	)

inline

Definition at line 91 of file vnl_rational.h.

◆ vnl_rational() [4/16]

vnl_rational::vnl_rational ( unsigned long num )

inline

Definition at line 94 of file vnl_rational.h.

◆ vnl_rational() [5/16]

vnl_rational::vnl_rational	(	unsigned long	num,
		unsigned long	den
	)

inline

Definition at line 96 of file vnl_rational.h.

◆ vnl_rational() [6/16]

vnl_rational::vnl_rational ( int num )

inline

Definition at line 99 of file vnl_rational.h.

◆ vnl_rational() [7/16]

vnl_rational::vnl_rational	(	int	num,
		int	den
	)

inline

Definition at line 101 of file vnl_rational.h.

◆ vnl_rational() [8/16]

vnl_rational::vnl_rational ( unsigned int num )

inline

Definition at line 104 of file vnl_rational.h.

◆ vnl_rational() [9/16]

vnl_rational::vnl_rational	(	unsigned int	num,
		unsigned int	den
	)

inline

Definition at line 106 of file vnl_rational.h.

◆ vnl_rational() [10/16]

vnl_rational::vnl_rational ( short num )

inline

Definition at line 109 of file vnl_rational.h.

◆ vnl_rational() [11/16]

vnl_rational::vnl_rational	(	short	num,
		short	den
	)

inline

Definition at line 111 of file vnl_rational.h.

◆ vnl_rational() [12/16]

vnl_rational::vnl_rational ( unsigned short num )

inline

Definition at line 114 of file vnl_rational.h.

◆ vnl_rational() [13/16]

vnl_rational::vnl_rational	(	unsigned short	num,
		unsigned short	den
	)

inline

Definition at line 116 of file vnl_rational.h.

◆ vnl_rational() [14/16]

vnl_rational::vnl_rational ( double d )

Creates a rational from a double.

This is done by computing the continued fraction approximation for d. Note that this is explicitly not an automatic type conversion.

This is done by computing the continued fraction approximation for d.

Definition at line 33 of file vnl_rational.cxx.

◆ vnl_rational() [15/16]

vnl_rational::vnl_rational ( float f )

Creates a rational from a double.

This is done by computing the continued fraction approximation for d.

Definition at line 40 of file vnl_rational.cxx.

◆ vnl_rational() [16/16]

vnl_rational::vnl_rational ( vnl_rational const & from )

inline

Definition at line 125 of file vnl_rational.h.

◆ ~vnl_rational()

vnl_rational::~vnl_rational ( )

inlinedefault

Member Function Documentation

◆ abs()

vnl_rational vnl_rational::abs ( ) const

inline

Returns the absolute value of the current rational.

Definition at line 157 of file vnl_rational.h.

◆ ceil()

long vnl_rational::ceil ( ) const

inline

Converts rational value to integer by truncating towards positive infinity.

Definition at line 255 of file vnl_rational.h.

◆ denominator()

long vnl_rational::denominator ( ) const

inline

Return the denominator of the (simplified) rational number representation.

Definition at line 135 of file vnl_rational.h.

◆ floor()

long vnl_rational::floor ( ) const

inline

Converts rational value to integer by truncating towards negative infinity.

Definition at line 252 of file vnl_rational.h.

◆ gcd()

static long vnl_rational::gcd	(	long	l1,
		long	l2
	)

inlinestatic

Calculate greatest common divisor of two integers.

Used to simplify rational number.

Definition at line 283 of file vnl_rational.h.

◆ invert()

vnl_rational& vnl_rational::invert ( )

inline

Replaces rational with 1/rational and returns it.

Inverting 0 gives +Inf, inverting +-Inf gives 0.

Definition at line 160 of file vnl_rational.h.

◆ normalize()

void vnl_rational::normalize ( )

inlineprivate

Private function to normalize numerator/denominator of rational number.

If num_ and den_ are both nonzero, their gcd is made 1 and den_ made positive. Otherwise, the nonzero den_ is set to 1 or the nonzero num_ to +1 or -1.

Definition at line 292 of file vnl_rational.h.

◆ numerator()

long vnl_rational::numerator ( ) const

inline

Return the numerator of the (simplified) rational number representation.

Definition at line 133 of file vnl_rational.h.

◆ operator *=() [1/2]

vnl_rational & vnl_rational::operator *= ( vnl_rational const & r )

Multiply/assign: replace lhs by lhs * rhs.

Note that 0 * Inf and Inf * 0 are undefined. Also note that there could be integer overflow during this calculation! In that case, an approximate result will be returned.

Definition at line 49 of file vnl_rational.cxx.

◆ operator *=() [2/2]

vnl_rational & vnl_rational::operator *= ( long r )

Multiply/assign: replace lhs by lhs * rhs.

Note that there could be integer overflow during this calculation! In that case, an approximate result will be returned.

Definition at line 68 of file vnl_rational.cxx.

◆ operator double() [1/2]

vnl_rational::operator double ( ) const

inline

Definition at line 278 of file vnl_rational.h.

◆ operator double() [2/2]

vnl_rational::operator double ( )

inline

Definition at line 279 of file vnl_rational.h.

◆ operator float() [1/2]

vnl_rational::operator float ( ) const

inline

Definition at line 276 of file vnl_rational.h.

◆ operator float() [2/2]

vnl_rational::operator float ( )

inline

Definition at line 277 of file vnl_rational.h.

◆ operator int()

vnl_rational::operator int ( )

inline

Definition at line 269 of file vnl_rational.h.

◆ operator long() [1/2]

vnl_rational::operator long ( ) const

inline

Definition at line 274 of file vnl_rational.h.

◆ operator long() [2/2]

vnl_rational::operator long ( )

inline

Definition at line 275 of file vnl_rational.h.

◆ operator short()

vnl_rational::operator short ( )

inline

Definition at line 264 of file vnl_rational.h.

◆ operator!()

bool vnl_rational::operator! ( ) const

inline

Unary not - returns true if rational is equal to zero.

Definition at line 155 of file vnl_rational.h.

◆ operator!=() [1/3]

bool vnl_rational::operator!= ( vnl_rational const & rhs ) const

inline

Definition at line 144 of file vnl_rational.h.

◆ operator!=() [2/3]

bool vnl_rational::operator!= ( long rhs ) const

inline

Definition at line 146 of file vnl_rational.h.

◆ operator!=() [3/3]

bool vnl_rational::operator!= ( int rhs ) const

inline

Definition at line 148 of file vnl_rational.h.

◆ operator%=() [1/2]

vnl_rational& vnl_rational::operator%= ( vnl_rational const & r )

inline

Modulus/assign: replace lhs by lhs % rhs.

Note that r % Inf is r, and that r % 0 and Inf % r are undefined.

Definition at line 206 of file vnl_rational.h.

◆ operator%=() [2/2]

vnl_rational& vnl_rational::operator%= ( long r )

inline

Definition at line 215 of file vnl_rational.h.

◆ operator+()

vnl_rational vnl_rational::operator+ ( ) const

inline

Unary plus - returns the current rational.

Definition at line 153 of file vnl_rational.h.

◆ operator++() [1/2]

vnl_rational& vnl_rational::operator++ ( )

inline

Pre-increment (++r). No-op when +-Inf.

Definition at line 218 of file vnl_rational.h.

◆ operator++() [2/2]

vnl_rational vnl_rational::operator++ ( int )

inline

Post-increment (r++). No-op when +-Inf.

Definition at line 222 of file vnl_rational.h.

◆ operator+=() [1/2]

vnl_rational& vnl_rational::operator+= ( vnl_rational const & r )

inline

Plus/assign: replace lhs by lhs + rhs.

Note that +Inf + -Inf and -Inf + +Inf are undefined.

Definition at line 165 of file vnl_rational.h.

◆ operator+=() [2/2]

vnl_rational& vnl_rational::operator+= ( long r )

inline

Definition at line 173 of file vnl_rational.h.

◆ operator-()

vnl_rational vnl_rational::operator- ( ) const

inline

Unary minus - returns the negation of the current rational.

Definition at line 151 of file vnl_rational.h.

◆ operator--() [1/2]

vnl_rational& vnl_rational::operator-- ( )

inline

Pre-decrement (–r). No-op when +-Inf.

Definition at line 220 of file vnl_rational.h.

◆ operator--() [2/2]

vnl_rational vnl_rational::operator-- ( int )

inline

Post-decrement (r–). No-op when +-Inf.

Definition at line 224 of file vnl_rational.h.

◆ operator-=() [1/2]

vnl_rational& vnl_rational::operator-= ( vnl_rational const & r )

inline

Minus/assign: replace lhs by lhs - rhs.

Note that +Inf - +Inf and -Inf - -Inf are undefined.

Definition at line 176 of file vnl_rational.h.

◆ operator-=() [2/2]

vnl_rational& vnl_rational::operator-= ( long r )

inline

Definition at line 184 of file vnl_rational.h.

◆ operator/=() [1/2]

vnl_rational & vnl_rational::operator/= ( vnl_rational const & r )

Divide/assign: replace lhs by lhs / rhs.

Note that 0 / 0 and Inf / Inf are undefined. Also note that there could be integer overflow during this calculation! In that case, an approximate result will be returned.

Definition at line 84 of file vnl_rational.cxx.

◆ operator/=() [2/2]

vnl_rational & vnl_rational::operator/= ( long r )

Divide/assign: replace lhs by lhs / rhs.

Note that 0 / 0 is undefined. Also note that there could be integer overflow during this calculation! In that case, an approximate result will be returned.

Definition at line 104 of file vnl_rational.cxx.

◆ operator<() [1/4]

bool vnl_rational::operator< ( vnl_rational const & rhs ) const

inline

Definition at line 226 of file vnl_rational.h.

◆ operator<() [2/4]

bool vnl_rational::operator< ( long r ) const

inline

Definition at line 236 of file vnl_rational.h.

◆ operator<() [3/4]

bool vnl_rational::operator< ( int r ) const

inline

Definition at line 240 of file vnl_rational.h.

◆ operator<() [4/4]

bool vnl_rational::operator< ( double r ) const

inline

Definition at line 244 of file vnl_rational.h.

◆ operator<=() [1/4]

bool vnl_rational::operator<= ( vnl_rational const & r ) const

inline

Definition at line 234 of file vnl_rational.h.

◆ operator<=() [2/4]

bool vnl_rational::operator<= ( long r ) const

inline

Definition at line 238 of file vnl_rational.h.

◆ operator<=() [3/4]

bool vnl_rational::operator<= ( int r ) const

inline

Definition at line 242 of file vnl_rational.h.

◆ operator<=() [4/4]

bool vnl_rational::operator<= ( double r ) const

inline

Definition at line 246 of file vnl_rational.h.

◆ operator=()

vnl_rational& vnl_rational::operator= ( vnl_rational const & rhs )

inline

Copies the contents and state of rhs rational over to the lhs.

Definition at line 138 of file vnl_rational.h.

◆ operator==() [1/3]

bool vnl_rational::operator== ( vnl_rational const & rhs ) const

inline

Returns true if the two rationals have the same representation.

Definition at line 142 of file vnl_rational.h.

◆ operator==() [2/3]

bool vnl_rational::operator== ( long rhs ) const

inline

Definition at line 145 of file vnl_rational.h.

◆ operator==() [3/3]

bool vnl_rational::operator== ( int rhs ) const

inline

Definition at line 147 of file vnl_rational.h.

◆ operator>() [1/4]

bool vnl_rational::operator> ( vnl_rational const & r ) const

inline

Definition at line 233 of file vnl_rational.h.

◆ operator>() [2/4]

bool vnl_rational::operator> ( long r ) const

inline

Definition at line 237 of file vnl_rational.h.

◆ operator>() [3/4]

bool vnl_rational::operator> ( int r ) const

inline

Definition at line 241 of file vnl_rational.h.

◆ operator>() [4/4]

bool vnl_rational::operator> ( double r ) const

inline

Definition at line 245 of file vnl_rational.h.

◆ operator>=() [1/4]

bool vnl_rational::operator>= ( vnl_rational const & r ) const

inline

Definition at line 235 of file vnl_rational.h.

◆ operator>=() [2/4]

bool vnl_rational::operator>= ( long r ) const

inline

Definition at line 239 of file vnl_rational.h.

◆ operator>=() [3/4]

bool vnl_rational::operator>= ( int r ) const

inline

Definition at line 243 of file vnl_rational.h.

◆ operator>=() [4/4]

bool vnl_rational::operator>= ( double r ) const

inline

Definition at line 247 of file vnl_rational.h.

◆ round()

long vnl_rational::round ( ) const

inline

Rounds rational to nearest integer.

Definition at line 258 of file vnl_rational.h.

◆ set()

void vnl_rational::set	(	long	num,
		long	den
	)

inline

Definition at line 130 of file vnl_rational.h.

◆ truncate()

long vnl_rational::truncate ( ) const

inline

Converts rational value to integer by truncating towards zero.

Definition at line 250 of file vnl_rational.h.

Friends And Related Function Documentation

◆ operator *()

vnl_rational operator *	(	vnl_rational const &	r1,
		vnl_rational const &	r2
	)

Definition at line 375 of file vnl_rational.h.

◆ operator%()

vnl_rational operator%	(	vnl_rational const &	r1,
		vnl_rational const &	r2
	)

Definition at line 429 of file vnl_rational.h.

◆ operator+()

vnl_rational operator+	(	vnl_rational const &	r1,
		vnl_rational const &	r2
	)

Definition at line 321 of file vnl_rational.h.

◆ operator-()

vnl_rational operator-	(	vnl_rational const &	r1,
		vnl_rational const &	r2
	)

Definition at line 348 of file vnl_rational.h.

◆ operator/()

vnl_rational operator/	(	vnl_rational const &	r1,
		vnl_rational const &	r2
	)

Definition at line 402 of file vnl_rational.h.

◆ operator<<()

std::ostream & operator<<	(	std::ostream &	s,
		vnl_rational const &	r
	)

Definition at line 306 of file vnl_rational.h.

◆ operator>>()

std::istream & operator>>	(	std::istream &	s,
		vnl_rational &	r
	)

Definition at line 313 of file vnl_rational.h.

◆ vsl_b_read()

void vsl_b_read	(	vsl_b_istream &	is,
		vnl_rational &	v
	)

Definition at line 20 of file vnl_io_rational.cxx.

◆ vsl_b_write()

void vsl_b_write	(	vsl_b_ostream &	os,
		vnl_rational const &	v
	)

Definition at line 10 of file vnl_io_rational.cxx.

◆ vsl_print_summary()

void vsl_print_summary	(	std::ostream &	os,
		vnl_rational const &	b
	)

Definition at line 44 of file vnl_io_rational.cxx.

Member Data Documentation

◆ den_

long vnl_rational::den_

private

Denominator portion.

Definition at line 77 of file vnl_rational.h.

◆ num_

long vnl_rational::num_

private

Numerator portion.

Definition at line 76 of file vnl_rational.h.

The documentation for this class was generated from the following files:

core/vnl/vnl_rational.h
core/vnl/io/vnl_io_rational.h
core/vnl/vnl_rational.cxx

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Related Functions

Detailed Description

Constructor & Destructor Documentation

◆ vnl_rational() [1/16]

◆ vnl_rational() [2/16]

◆ vnl_rational() [3/16]

◆ vnl_rational() [4/16]

◆ vnl_rational() [5/16]

◆ vnl_rational() [6/16]

◆ vnl_rational() [7/16]

◆ vnl_rational() [8/16]

◆ vnl_rational() [9/16]

◆ vnl_rational() [10/16]

◆ vnl_rational() [11/16]

◆ vnl_rational() [12/16]

◆ vnl_rational() [13/16]

◆ vnl_rational() [14/16]

◆ vnl_rational() [15/16]

◆ vnl_rational() [16/16]

◆ ~vnl_rational()

Member Function Documentation

◆ abs()

◆ ceil()

◆ denominator()

◆ floor()

◆ gcd()

◆ invert()

◆ normalize()

◆ numerator()

◆ operator *=() [1/2]

◆ operator *=() [2/2]

◆ operator double() [1/2]

◆ operator double() [2/2]

◆ operator float() [1/2]

◆ operator float() [2/2]

◆ operator int()

◆ operator long() [1/2]

◆ operator long() [2/2]

◆ operator short()

◆ operator!()

◆ operator!=() [1/3]

◆ operator!=() [2/3]

◆ operator!=() [3/3]

◆ operator%=() [1/2]

◆ operator%=() [2/2]

◆ operator+()

◆ operator++() [1/2]

◆ operator++() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-()

◆ operator--() [1/2]

◆ operator--() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator<() [1/4]

◆ operator<() [2/4]

◆ operator<() [3/4]

◆ operator<() [4/4]

◆ operator<=() [1/4]

◆ operator<=() [2/4]

◆ operator<=() [3/4]

◆ operator<=() [4/4]

◆ operator=()

◆ operator==() [1/3]

◆ operator==() [2/3]

◆ operator==() [3/3]

◆ operator>() [1/4]

◆ operator>() [2/4]

◆ operator>() [3/4]

◆ operator>() [4/4]

◆ operator>=() [1/4]

◆ operator>=() [2/4]

◆ operator>=() [3/4]