Model of a fixed-precision rational number. More...

#include <rational.hpp>

Inheritance diagram for vnix::rat::rational< NB, DB >:

Collaboration diagram for vnix::rat::rational< NB, DB >:

Classes
struct	dummy_arg

Public Types
using	stype = typename int_types< BITS >::SS
	Signed type for encoding. More...

using	utype = typename int_types< BITS >::US
	Unsigned type for encoding. More...

Public Types inherited from vnix::rat::encoding< NB, DB >
enum

enum
	Mask for each of numerator and denominator. More...

using	utype = typename int_types< BITS >::US
	Unsigned type for encoding. More...

using	stype = typename int_types< BITS >::SS
	Signed type for encoding. More...

using	uftype = typename int_types< BITS >::UF
	Unsigned fast type. More...

using	sftype = typename int_types< BITS >::SF
	Signed fast type. More...

Public Member Functions
constexpr	rational (stype n=0, stype d=1)
	Initialize from numerator and denominator. More...

template<unsigned ONB, unsigned ODB>
constexpr	rational (rational< ONB, ODB > r)
	Initialize from other rational. More...

constexpr stype	to_int () const
	Convert to (signed) integer. More...

constexpr bool	to_bool () const
	Automatically convert to boolean. More...

constexpr float	to_float () const
	Convert to float. More...

constexpr double	to_double () const
	Convert to double. More...

template<unsigned ONB, unsigned ODB>
constexpr rational &	operator+= (rational< ONB, ODB > r)
	Modify this rational number by adding other rational number. More...

template<unsigned ONB, unsigned ODB>
constexpr rational &	operator-= (rational< ONB, ODB > r)
	Modify this rational number by subtracting other rational number. More...

constexpr rational	reciprocal () const
	Reciprocal of this rational number. More...

template<unsigned ONB, unsigned ODB>
constexpr rational &	operator*= (rational< ONB, ODB > r)
	Modify this rational number by multiplying by other rational number. More...

template<unsigned ONB, unsigned ODB>
constexpr rational &	operator/= (rational< ONB, ODB > r)
	Modify this rational number by dividing by other rational number. More...

template<unsigned ONB, unsigned ODB>
constexpr rational< NB, DB > &	operator+= (rational< ONB, ODB > r)

template<unsigned ONB, unsigned ODB>
constexpr rational< NB, DB > &	operator-= (rational< ONB, ODB > r)

template<unsigned ONB, unsigned ODB>
constexpr rational< NB, DB > &	operator*= (rational< ONB, ODB > r)

template<unsigned ONB, unsigned ODB>
constexpr rational< NB, DB > &	operator/= (rational< ONB, ODB > r)

Public Member Functions inherited from vnix::rat::encoding< NB, DB >
constexpr	encoding (normalized_pair< NMR_BITS, DNM_BITS > p)
	Initialize from normalized numerator and denominator. More...

constexpr int_types< NMR_BITS >::SF	n () const
	Normalized numerator. More...

constexpr int_types< DNM_BITS >::UF	d () const
	Normalized denominator. More...

Static Public Member Functions
static constexpr utype	encode (rational r)
	Encoding from rational number. More...

static constexpr rational	decode (utype u)
	Rational number from encoding. More...

Private Types
using	P = encoding< NB, DB >

Private Member Functions
constexpr	rational (utype u, dummy_arg)
	Construct from encoding. More...

Additional Inherited Members
Protected Member Functions inherited from vnix::rat::encoding< NB, DB >
constexpr	encoding (utype c)
	Allow descendant to construct from code-word. More...

Protected Attributes inherited from vnix::rat::encoding< NB, DB >
utype	c_
	Unsigned word storing encoding. More...

Detailed Description

template<unsigned NB, unsigned DB>
class vnix::rat::rational< NB, DB >

Model of a fixed-precision rational number.

Numerator and denominator are encoded in same unsigned integer word. They form a partition of the bits in the word.

Template Parameters

NB	Number of bits for numerator.
DB	Number of bits for denominator.

Definition at line 27 of file rational.hpp.

Member Typedef Documentation

template<unsigned NB, unsigned DB>

using vnix::rat::rational< NB, DB >::P = encoding<NB, DB>

private

Definition at line 29 of file rational.hpp.

template<unsigned NB, unsigned DB>

using vnix::rat::encoding< NMR_BITS, DNM_BITS >::stype = typename int_types<BITS>::SS

Signed type for encoding.

Definition at line 23 of file encoding.hpp.

template<unsigned NB, unsigned DB>

using vnix::rat::encoding< NMR_BITS, DNM_BITS >::utype = typename int_types<BITS>::US

Unsigned type for encoding.

Definition at line 22 of file encoding.hpp.

Constructor & Destructor Documentation

template<unsigned NB, unsigned DB>

constexpr vnix::rat::rational< NB, DB >::rational	(	utype	u,
		dummy_arg
	)

inlineprivate

Construct from encoding.

Parameters

u	Encoding of rational number.

Definition at line 38 of file rational.hpp.

38 : P(u) {}

vnix::rat::rational::P

encoding< NB, DB > P

Definition: rational.hpp:29

template<unsigned NB, unsigned DB>

constexpr vnix::rat::rational< NB, DB >::rational	(	stype	n = `0`,
		stype	d = `1`
	)

inline

Initialize from numerator and denominator.

Parameters

n	Numerator (zero by default).
d	Denominator (unity by default).

Definition at line 47 of file rational.hpp.

48 : P(normalized_pair<NB, DB>(n, d)) {}

vnix::rat::normalized_pair

Numerator and denominator of a rational number as separate numbers, not encoded into the same word...

Definition: normalized-pair.hpp:25

vnix::rat::encoding< NB, DB >::d

constexpr int_types< DNM_BITS >::UF d() const

Normalized denominator.

Definition: encoding.hpp:68

vnix::rat::rational::P

encoding< NB, DB > P

Definition: rational.hpp:29

vnix::rat::encoding< NB, DB >::n

constexpr int_types< NMR_BITS >::SF n() const

Normalized numerator.

Definition: encoding.hpp:55

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template<unsigned NB, unsigned DB>

template<unsigned ONB, unsigned ODB>

constexpr vnix::rat::rational< NB, DB >::rational ( rational< ONB, ODB > r )

inline

Initialize from other rational.

Template Parameters

ONB	Number of numerator-bits in other type of rational.
ODB	Number of denominator-bits in other type of rational.

Parameters

r	Copy of other rational.

Definition at line 55 of file rational.hpp.

56 : P(normalized_pair<NB, DB>(r.n(), r.d())) {}

vnix::rat::normalized_pair

Numerator and denominator of a rational number as separate numbers, not encoded into the same word...

Definition: normalized-pair.hpp:25

vnix::rat::rational::P

encoding< NB, DB > P

Definition: rational.hpp:29

Member Function Documentation

template<unsigned NB, unsigned DB>

static constexpr rational vnix::rat::rational< NB, DB >::decode ( utype u )

inlinestatic

Rational number from encoding.

Definition at line 116 of file rational.hpp.

116 { return {u, dummy_arg()}; }

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template<unsigned NB, unsigned DB>

static constexpr utype vnix::rat::rational< NB, DB >::encode ( rational< NB, DB > r )

inlinestatic

Encoding from rational number.

Definition at line 113 of file rational.hpp.

113 { return r.c_; }

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template<unsigned NB, unsigned DB>

template<unsigned ONB, unsigned ODB>

constexpr rational& vnix::rat::rational< NB, DB >::operator*= ( rational< ONB, ODB > r )

Modify this rational number by multiplying by other rational number.

Template Parameters

ONB	Number of numerator -bits in other rational.
ODB	Number of denominator-bits in other rational.

Parameters

r	Other rational number.

Returns: Reference to this rational number (after multiplication).

template<unsigned NB, unsigned DB>

template<unsigned ONB, unsigned ODB>

constexpr rational<NB, DB>& vnix::rat::rational< NB, DB >::operator*= ( rational< ONB, ODB > r )

Definition at line 323 of file rational.hpp.

                                                              {
   return *this = (*this) * r;
 }

template<unsigned NB, unsigned DB>

template<unsigned ONB, unsigned ODB>

constexpr rational& vnix::rat::rational< NB, DB >::operator+= ( rational< ONB, ODB > r )

Modify this rational number by adding other rational number.

Template Parameters

ONB	Number of numerator -bits in other rational.
ODB	Number of denominator-bits in other rational.

Parameters

r	Other rational number.

Returns: Reference to this rational number (after addition).

template<unsigned NB, unsigned DB>

template<unsigned ONB, unsigned ODB>

constexpr rational<NB, DB>& vnix::rat::rational< NB, DB >::operator+= ( rational< ONB, ODB > r )

Definition at line 241 of file rational.hpp.

                                                              {
   return *this = *this + r;
 }

template<unsigned NB, unsigned DB>

template<unsigned ONB, unsigned ODB>

constexpr rational& vnix::rat::rational< NB, DB >::operator-= ( rational< ONB, ODB > r )

Modify this rational number by subtracting other rational number.

Template Parameters

ONB	Number of numerator -bits in other rational.
ODB	Number of denominator-bits in other rational.

Parameters

r	Other rational number.

Returns: Reference to this rational number (after subtraction).

template<unsigned NB, unsigned DB>

template<unsigned ONB, unsigned ODB>

constexpr rational<NB, DB>& vnix::rat::rational< NB, DB >::operator-= ( rational< ONB, ODB > r )

Definition at line 264 of file rational.hpp.

                                                              {
   return *this = *this - r;
 }

template<unsigned NB, unsigned DB>

template<unsigned ONB, unsigned ODB>

constexpr rational& vnix::rat::rational< NB, DB >::operator/= ( rational< ONB, ODB > r )

Modify this rational number by dividing by other rational number.

Template Parameters

ONB	Number of numerator -bits in other rational.
ODB	Number of denominator-bits in other rational.

Parameters

r	Other rational number.

Returns: Reference to this rational number (after division).

template<unsigned NB, unsigned DB>

template<unsigned ONB, unsigned ODB>

constexpr rational<NB, DB>& vnix::rat::rational< NB, DB >::operator/= ( rational< ONB, ODB > r )

Definition at line 332 of file rational.hpp.

                                                              {
   return *this = (*this) / r;
 }

template<unsigned NB, unsigned DB>

constexpr rational vnix::rat::rational< NB, DB >::reciprocal ( ) const

inline

Reciprocal of this rational number.

Definition at line 90 of file rational.hpp.

                                         {
     if (n() == 0) { throw "attempt to take reciprocal of zero"; }
     if (n() < 0) { return rational(-d(), -n()); }
     return rational(d(), n());
   }

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template<unsigned NB, unsigned DB>

constexpr bool vnix::rat::rational< NB, DB >::to_bool ( ) const

inline

Automatically convert to boolean.

Definition at line 65 of file rational.hpp.

65 { return n() != 0; }

vnix::rat::encoding< NB, DB >::n

constexpr int_types< NMR_BITS >::SF n() const

Normalized numerator.

Definition: encoding.hpp:55

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template<unsigned NB, unsigned DB>

constexpr double vnix::rat::rational< NB, DB >::to_double ( ) const

inline

Convert to double.

Definition at line 71 of file rational.hpp.

71 { return n() * 1.0 / d(); }

vnix::rat::encoding< NB, DB >::d

constexpr int_types< DNM_BITS >::UF d() const

Normalized denominator.

Definition: encoding.hpp:68

vnix::rat::encoding< NB, DB >::n

constexpr int_types< NMR_BITS >::SF n() const

Normalized numerator.

Definition: encoding.hpp:55

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template<unsigned NB, unsigned DB>

constexpr float vnix::rat::rational< NB, DB >::to_float ( ) const

inline

Convert to float.

Definition at line 68 of file rational.hpp.

68 { return n() * 1.0f / d(); }

vnix::rat::encoding< NB, DB >::d

constexpr int_types< DNM_BITS >::UF d() const

Normalized denominator.

Definition: encoding.hpp:68

vnix::rat::encoding< NB, DB >::n

constexpr int_types< NMR_BITS >::SF n() const

Normalized numerator.

Definition: encoding.hpp:55

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template<unsigned NB, unsigned DB>

constexpr stype vnix::rat::rational< NB, DB >::to_int ( ) const

inline

Convert to (signed) integer.

Definition at line 59 of file rational.hpp.

                                  {
     if (d() != 1) { throw "attempted conversion to integer from fraction"; }
     return n();
   }

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

vnix/rat/rational.hpp

Classes

Public Types

Public Member Functions

Static Public Member Functions

Private Types

Private Member Functions

Additional Inherited Members

Detailed Description

template<unsigned NB, unsigned DB> class vnix::rat::rational< NB, DB >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<unsigned NB, unsigned DB>
class vnix::rat::rational< NB, DB >