rational< T > Class Template Reference

Represent a rational number (fraction) as a numerator and denominator. More...

#include <rational.hpp>

Public Types
typedef T	value_type
	Convenience typedef for the integral type of the numerator and denominator. More...

Public Member Functions
	rational (value_type num=0)
	rational (value_type num, value_type den)
	rational (double r)
template<class U >
	rational (rational< U > const &that)
	Copy from a different type of rational. More...
value_type	numerator () const
	Return the numerator. More...
value_type	denominator () const
	Return the denominator. More...
template<class U , class EnableIfFloat = typename std::enable_if<std::is_floating_point<U>::value>::type>
	operator U () const
	Convert the rational number to a floating-point type. More...
rational &	operator= (value_type)
	Assignment of an integer. More...
template<class U >
rational &	operator= (rational< U > const &rhs)
	Assignment of a rational with a different size. More...
rational &	operator+= (rational const &rhs)
	Addition assignment operator. More...
rational &	operator+= (value_type const &rhs)
	Addition assignment operator. More...
rational &	operator-= (rational const &rhs)
	Subtraction assignment operator. More...
rational &	operator-= (value_type const &rhs)
	Subtraction assignment operator. More...
rational &	operator*= (rational const &rhs)
	Multiplication assignment operator. More...
rational &	operator*= (value_type const &rhs)
	Multiplication assignment operator. More...
rational &	operator/= (rational const &rhs)
	Division assignment operator. More...
rational &	operator/= (value_type const &rhs)
	Division assignment operator. More...
rational &	operator++ ()
	Pre-increment. More...
rational &	operator-- ()
	Pre-decrement. More...
rational	operator++ (int)
	Post-increment. More...
rational	operator-- (int)
	Post-decrement. More...
template<class U >
T	scale (U value)
template<class U >
rational< T > &	operator= (rational< U > const &rhs)

Private Member Functions
void	reduce ()
	Reduce the numerator and denominator by their GCD. More...
void	normalize ()
template<class U >
value_type	scale (U value)

Private Attributes
value_type	numerator_
value_type	denominator_

Static Private Attributes
static constexpr value_type	double_divisor = power10<value_type>(std::numeric_limits<value_type>::digits10 - 1)

Detailed Description

template<class T>
class rational< T >

Represent a rational number (fraction) as a numerator and denominator.

Definition at line 26 of file rational.hpp.

Member Typedef Documentation

template<class T>

typedef T rational< T >::value_type

Convenience typedef for the integral type of the numerator and denominator.

Definition at line 30 of file rational.hpp.

Constructor & Destructor Documentation

template<class T>

rational< T >::rational ( value_type  num = 0 )

inline

Default constructor and constructor from a single value. As a default constructor, initializes to zero. Otherwise, initializes to the integer num.

Parameters

num	The integer value to use as the initial value

Definition at line 36 of file rational.hpp.

: numerator_{num}, denominator_{1} {}

template<class T >

rational< T >::rational	(	value_type	num,
		value_type	den
	)

Construct a rational number

Parameters

num	numerator
den	denominator

Exceptions

zero_denominator

if den == 0

Definition at line 113 of file rational.hpp.

: numerator_{num},
  denominator_{den == value_type{} ? throw zero_denominator{"zero denominator"} : den}
{
  normalize();
}

template<class T >

rational< T >::rational

(

double

r

)

Initialize the rational number with an approximation of r

Parameters

r	the initial value

Definition at line 121 of file rational.hpp.

References rational< T >::double_divisor.

: numerator_{static_cast<T>(r / double_divisor + 0.5)}, denominator_{double_divisor}
{}

template<class T >

template<class U >

rational< T >::rational

(

rational< U > const &

that

)

Copy from a different type of rational.

Definition at line 127 of file rational.hpp.

References rational< T >::denominator(), rational< T >::denominator_, rational< T >::numerator(), and rational< T >::reduce().

: numerator_{scale<U>(that.numerator())}, denominator_{scale<U>(that.denominator())}
{
  reduce();
}

Member Function Documentation

template<class T>

value_type rational< T >::denominator ( ) const

inline

Return the denominator.

Definition at line 52 of file rational.hpp.

Referenced by absval(), number_rational::do_divide(), rational< long long >::operator U(), rational< T >::operator*=(), rational< T >::operator++(), rational< T >::operator+=(), operator-(), rational< T >::operator--(), rational< T >::operator-=(), operator/(), rational< T >::operator/=(), rational< T >::operator=(), operator==(), rational< T >::rational(), and rational< T >::reduce().

{ return denominator_; }

template<class T >

void rational< T >::normalize ( )

private

Reduce the numerator and denominator, and normalize the signs of both, that is, ensure denominator is not negative.

Definition at line 144 of file rational.hpp.

References rational< T >::denominator_, rational< T >::numerator_, and rational< T >::reduce().

Referenced by rational< T >::operator/=().

{
  if (denominator_ < value_type{})
  {
    denominator_ = -denominator_;
    numerator_ = -numerator_;
  }
  reduce();
}

template<class T>

value_type rational< T >::numerator ( ) const

inline

Return the numerator.

Definition at line 50 of file rational.hpp.

Referenced by absval(), number_rational::do_divide(), rational< long long >::operator U(), rational< T >::operator*=(), rational< T >::operator+=(), operator-(), rational< T >::operator-=(), operator/(), rational< T >::operator/=(), operator<(), operator<<(), rational< T >::operator=(), operator==(), rational< T >::rational(), and rational< T >::reduce().

{ return numerator_; }

template<class T>

template<class U , class EnableIfFloat = typename std::enable_if<std::is_floating_point<U>::value>::type>

rational< T >::operator U ( ) const

inlineexplicit

Convert the rational number to a floating-point type.

Definition at line 55 of file rational.hpp.

{ return static_cast<U>(numerator()) / denominator(); }

template<class T >

rational< T > & rational< T >::operator*=

(

rational< T > const &

rhs

)

Multiplication assignment operator.

Definition at line 217 of file rational.hpp.

References rational< T >::denominator(), rational< T >::denominator_, rational< T >::numerator(), rational< T >::numerator_, and rational< T >::reduce().

{
  numerator_ *= rhs.numerator();
  denominator_ *= rhs.denominator();
  reduce();
  return *this;
}

template<class T >

rational< T > & rational< T >::operator*=

(

value_type const &

rhs

)

Multiplication assignment operator.

Definition at line 226 of file rational.hpp.

References rational< T >::numerator_, and rational< T >::reduce().

{
  numerator_ *= rhs;
  reduce();
  return *this;
}

template<class T >

rational< T > & rational< T >::operator++

(

)

Pre-increment.

Definition at line 255 of file rational.hpp.

References rational< T >::denominator(), and rational< T >::numerator_.

{
  numerator_ += denominator();
  return *this;
}

template<class T >

rational< T > rational< T >::operator++

(

int

)

Post-increment.

Definition at line 262 of file rational.hpp.

{
  rational result(*this);
  ++*this;
  return result;
}

template<class T >

rational< T > & rational< T >::operator+=

(

rational< T > const &

rhs

)

Addition assignment operator.

Definition at line 183 of file rational.hpp.

References rational< T >::denominator(), rational< T >::denominator_, rational< T >::numerator(), rational< T >::numerator_, and rational< T >::reduce().

{
  numerator_ = numerator() * rhs.denominator() + rhs.numerator() * denominator();
  denominator_ *= rhs.denominator();
  reduce();
  return *this;
}

template<class T >

rational< T > & rational< T >::operator+=

(

value_type const &

rhs

)

Addition assignment operator.

Definition at line 192 of file rational.hpp.

References rational< T >::denominator(), rational< T >::numerator(), rational< T >::numerator_, and rational< T >::reduce().

{
  numerator_ = numerator() + rhs * denominator();
  reduce();
  return *this;
}

template<class T >

rational< T > & rational< T >::operator--

(

)

Pre-decrement.

Definition at line 270 of file rational.hpp.

References rational< T >::denominator(), and rational< T >::numerator_.

{
  numerator_ -= denominator();
  return *this;
}

template<class T >

rational< T > rational< T >::operator--

(

int

)

Post-decrement.

Definition at line 277 of file rational.hpp.

{
  rational result(*this);
  --*this;
  return result;
}

template<class T >

rational< T > & rational< T >::operator-=

(

rational< T > const &

rhs

)

Subtraction assignment operator.

Definition at line 200 of file rational.hpp.

References rational< T >::denominator(), rational< T >::denominator_, rational< T >::numerator(), rational< T >::numerator_, and rational< T >::reduce().

{
  numerator_ = numerator() * rhs.denominator() - rhs.numerator() * denominator();
  denominator_ *= rhs.denominator();
  reduce();
  return *this;
}

template<class T >

rational< T > & rational< T >::operator-=

(

value_type const &

rhs

)

Subtraction assignment operator.

Definition at line 209 of file rational.hpp.

References rational< T >::denominator(), rational< T >::numerator(), rational< T >::numerator_, and rational< T >::reduce().

{
  numerator_ = numerator() - rhs * denominator();
  reduce();
  return *this;
}

template<class T >

rational< T > & rational< T >::operator/=

(

rational< T > const &

rhs

)

Division assignment operator.

Definition at line 234 of file rational.hpp.

References rational< T >::denominator(), rational< T >::denominator_, rational< T >::normalize(), rational< T >::numerator(), and rational< T >::numerator_.

{
  if (rhs.numerator() == value_type{})
    throw zero_denominator{"divide by zero"};
  numerator_ *= rhs.denominator();
  denominator_ *= rhs.numerator();
  normalize();
  return *this;
}

template<class T >

rational< T > & rational< T >::operator/=

(

value_type const &

rhs

)

Division assignment operator.

Definition at line 245 of file rational.hpp.

References rational< T >::denominator_, and rational< T >::normalize().

{
  if (rhs == value_type{})
    throw zero_denominator{"divide by zero"};
  denominator_ *= rhs;
  normalize();
  return *this;
}

template<class T >

rational< T > & rational< T >::operator=

(

value_type

num

)

Assignment of an integer.

Definition at line 165 of file rational.hpp.

References rational< T >::denominator_, and rational< T >::numerator_.

{
  numerator_ = num;
  denominator_ = value_type{1};
  return *this;
}

template<class T>

template<class U >

rational& rational< T >::operator=

(

rational< U > const &

rhs

)

Assignment of a rational with a different size.

template<class T>

template<class U >

rational<T>& rational< T >::operator=

(

rational< U > const &

rhs

)

Definition at line 174 of file rational.hpp.

References rational< T >::denominator(), rational< T >::denominator_, rational< T >::numerator(), rational< T >::numerator_, and rational< T >::reduce().

{
  numerator_ = scale<U>(rhs.numerator());
  denominator_ = scale<U>(rhs.denominator());
  reduce();
  return *this;
}

template<class T >

void rational< T >::reduce ( )

private

Reduce the numerator and denominator by their GCD.

Definition at line 155 of file rational.hpp.

References rational< T >::denominator(), rational< T >::denominator_, gcd(), rational< T >::numerator(), and rational< T >::numerator_.

Referenced by rational< T >::normalize(), rational< T >::operator*=(), rational< T >::operator+=(), rational< T >::operator-=(), rational< T >::operator=(), and rational< T >::rational().

{
  value_type div{gcd(numerator(), denominator())};
  if (div == value_type{})
    throw zero_denominator{"zero denominator"};
  numerator_ /= div;
  denominator_ /= div;
}

template<class T>

template<class U >

value_type rational< T >::scale ( U  value )

private

Scale an integer of type U to the value_type. If U has more digits than value_type shift value to the right.

template<class T>

template<class U >

T rational< T >::scale

(

U

value

)

Definition at line 135 of file rational.hpp.

{
  if (std::numeric_limits<T>::digits >= std::numeric_limits<U>::digits)
    return T{value};
  else
    return T{value >> (std::numeric_limits<U>::digits - std::numeric_limits<T>::digits)};
}

Member Data Documentation

template<class T>

value_type rational< T >::denominator_

private

Definition at line 109 of file rational.hpp.

Referenced by rational< long long >::denominator(), rational< T >::normalize(), rational< T >::operator*=(), rational< T >::operator+=(), rational< T >::operator-=(), rational< T >::operator/=(), rational< T >::operator=(), rational< T >::rational(), and rational< T >::reduce().

template<class T>

constexpr value_type rational< T >::double_divisor = power10<value_type>(std::numeric_limits<value_type>::digits10 - 1)

staticprivate

Compute the divisor to use when converting a double to rational. This is the largest power of 10 that value_type can represent.

Definition at line 106 of file rational.hpp.

Referenced by rational< T >::rational().

template<class T>

value_type rational< T >::numerator_

private

Definition at line 108 of file rational.hpp.

Referenced by rational< T >::normalize(), rational< long long >::numerator(), rational< T >::operator*=(), rational< T >::operator++(), rational< T >::operator+=(), rational< T >::operator--(), rational< T >::operator-=(), rational< T >::operator/=(), rational< T >::operator=(), and rational< T >::reduce().

---

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

• rational.hpp