rational.hpp File Reference

#include <istream>
#include <limits>
#include <ostream>
#include <sstream>
#include <stdexcept>
#include <string>
#include <type_traits>
#include "gcd.hpp"
#include "ioflags.hpp"
#include "power10.hpp"

Go to the source code of this file.

Classes
class	zero_denominator
	Exception class if the denominator is ever zero. More...
class	rational< T >
	Represent a rational number (fraction) as a numerator and denominator. More...

Functions
template<class T >
rational< T >	operator- (rational< T > const &r)
	Negate a rational number. More...
template<class T >
rational< T >	absval (rational< T > const &r)
template<class T >
rational< T >	operator+ (rational< T > lhs, rational< T > const &rhs)
	Addition. More...
template<class T >
rational< T >	operator+ (rational< T > lhs, T const &rhs)
	Addition. More...
template<class T >
rational< T >	operator+ (T const &lhs, rational< T > rhs)
	Addition. More...
template<class T >
rational< T >	operator- (rational< T > lhs, rational< T > const &rhs)
	Subtraction. More...
template<class T >
rational< T >	operator- (rational< T > lhs, T const &rhs)
	Subtraction. More...
template<class T >
rational< T >	operator- (T const &lhs, rational< T > rhs)
	Subtraction. More...
template<class T >
rational< T >	operator* (rational< T > lhs, rational< T > const &rhs)
	Multiplication. More...
template<class T >
rational< T >	operator* (rational< T > lhs, T const &rhs)
	Multiplication. More...
template<class T >
rational< T >	operator* (T const &lhs, rational< T > rhs)
	Multiplication. More...
template<class T >
rational< T >	operator/ (rational< T > lhs, rational< T > const &rhs)
	Division. More...
template<class T >
rational< T >	operator/ (rational< T > lhs, T const &rhs)
	Division. More...
template<class T >
rational< T >	operator/ (T const &lhs, rational< T > rhs)
	Division. More...
template<class T , class U >
bool	operator== (rational< T > const &a, rational< U > const &b)
	Equality comparison. More...
template<class T >
bool	operator== (rational< T > const &lhs, T rhs)
	Equality comparison. More...
template<class T >
bool	operator== (T lhs, rational< T > const &rhs)
	Equality comparison. More...
template<class T >
bool	operator< (rational< T > const &a, rational< T > const &b)
	Less-than comparison. More...
template<class T >
bool	operator< (rational< T > const &a, T const &b)
	Less-than comparison. More...
template<class T >
bool	operator< (T const &a, rational< T > const &b)
	Less-than comparison. More...
template<class T , class U >
bool	operator!= (rational< T > const &a, rational< U > const &b)
	Inequality comparison. More...
template<class T >
bool	operator!= (rational< T > const &a, T b)
	Inequality comparison. More...
template<class T >
bool	operator!= (T a, rational< T > const &b)
	Inequality comparison. More...
template<class T >
bool	operator<= (rational< T > const &a, rational< T > const &b)
	Less-than-or-equal comparison. More...
template<class T >
bool	operator<= (rational< T > const &a, T const &b)
	Less-than-or-equal comparison. More...
template<class T >
bool	operator<= (T const &a, rational< T > const &b)
	Less-than-or-equal comparison. More...
template<class T >
bool	operator> (rational< T > const &a, rational< T > const &b)
	Greater-than comparison. More...
template<class T >
bool	operator> (rational< T > const &a, T const &b)
	Greater-than comparison. More...
template<class T >
bool	operator> (T const &a, rational< T > const &b)
	Greater-than comparison. More...
template<class T >
bool	operator>= (rational< T > const &a, rational< T > const &b)
	Greater-than-or-equal comparison. More...
template<class T >
bool	operator>= (rational< T > const &a, T const &b)
	Greater-than-or-equal comparison. More...
template<class T >
bool	operator>= (T const &a, rational< T > const &b)
	Greater-than-or-equal comparison. More...
template<class T , class Char , class Traits >
std::basic_istream< Char, Traits > &	operator>> (std::basic_istream< Char, Traits > &in, rational< T > &rat)
	Input operator. More...
template<class T , class Char , class Traits >
std::basic_ostream< Char, Traits > &	operator<< (std::basic_ostream< Char, Traits > &out, rational< T > const &rat)
	Output operator. More...

Function Documentation

template<class T >

rational<T> absval

(

rational< T > const &

r

)

Definition at line 292 of file rational.hpp.

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

{
  using std::abs;
  return rational<T>{abs(r.numerator()), r.denominator()};
}

template<class T , class U >

bool operator!= ( rational< T > const &  a, rational< U > const &  b  )

inline

Inequality comparison.

Definition at line 442 of file rational.hpp.

{
  return not (a == b);
}

template<class T >

bool operator!= ( rational< T > const &  a, T  b  )

inline

Inequality comparison.

Definition at line 449 of file rational.hpp.

{
  return not (a == b);
}

template<class T >

bool operator!= ( T  a, rational< T > const &  b  )

inline

Inequality comparison.

Definition at line 456 of file rational.hpp.

{
  return not (a == b);
}

template<class T >

rational<T> operator*	(	rational< T >	lhs,
		rational< T > const &	rhs
	)

Multiplication.

Definition at line 349 of file rational.hpp.

{
  lhs *= rhs;
  return lhs;
}

template<class T >

rational<T> operator*	(	rational< T >	lhs,
		T const &	rhs
	)

Multiplication.

Definition at line 357 of file rational.hpp.

{
  lhs *= rhs;
  return lhs;
}

template<class T >

rational<T> operator*	(	T const &	lhs,
		rational< T >	rhs
	)

Multiplication.

Definition at line 365 of file rational.hpp.

{
  rhs *= lhs;
  return rhs;
}

template<class T >

rational<T> operator+	(	rational< T >	lhs,
		rational< T > const &	rhs
	)

Addition.

Definition at line 300 of file rational.hpp.

{
  lhs += rhs;
  return lhs;
}

template<class T >

rational<T> operator+	(	rational< T >	lhs,
		T const &	rhs
	)

Addition.

Definition at line 308 of file rational.hpp.

{
  lhs += rhs;
  return lhs;
}

template<class T >

rational<T> operator+	(	T const &	lhs,
		rational< T >	rhs
	)

Addition.

Definition at line 316 of file rational.hpp.

{
  rhs += lhs;
  return rhs;
}

template<class T >

rational<T> operator-

(

rational< T > const &

r

)

Negate a rational number.

Definition at line 286 of file rational.hpp.

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

{
  return rational<T>{-r.numerator(), r.denominator()};
}

template<class T >

rational<T> operator-	(	rational< T >	lhs,
		rational< T > const &	rhs
	)

Subtraction.

Definition at line 324 of file rational.hpp.

{
  lhs -= rhs;
  return lhs;
}

template<class T >

rational<T> operator-	(	rational< T >	lhs,
		T const &	rhs
	)

Subtraction.

Definition at line 332 of file rational.hpp.

{
  lhs -= rhs;
  return lhs;
}

template<class T >

rational<T> operator-	(	T const &	lhs,
		rational< T >	rhs
	)

Subtraction.

Definition at line 340 of file rational.hpp.

{
  // Gotta be a little tricky.
  rhs += -lhs;
  return -rhs;
}

template<class T >

rational<T> operator/	(	rational< T >	lhs,
		rational< T > const &	rhs
	)

Division.

Definition at line 373 of file rational.hpp.

{
  lhs /= rhs;
  return lhs;
}

template<class T >

rational<T> operator/	(	rational< T >	lhs,
		T const &	rhs
	)

Division.

Definition at line 381 of file rational.hpp.

{
  lhs /= rhs;
  return lhs;
}

template<class T >

rational<T> operator/	(	T const &	lhs,
		rational< T >	rhs
	)

Division.

Definition at line 389 of file rational.hpp.

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

{
  return rational<T>{lhs * rhs.denominator(), rhs.numerator()};
}

template<class T >

bool operator<	(	rational< T > const &	a,
		rational< T > const &	b
	)

Less-than comparison.

Definition at line 421 of file rational.hpp.

References rational< T >::numerator().

{
  return a.numerator() * b.denominator() < b.numerator() * a.denominator();
}

template<class T >

bool operator<	(	rational< T > const &	a,
		T const &	b
	)

Less-than comparison.

Definition at line 428 of file rational.hpp.

{
  return a.numerator() < b * a.denominator();
}

template<class T >

bool operator<	(	T const &	a,
		rational< T > const &	b
	)

Less-than comparison.

Definition at line 435 of file rational.hpp.

{
  return a * b.denominator() < b.numerator();
}

template<class T , class Char , class Traits >

std::basic_ostream<Char, Traits>& operator<<	(	std::basic_ostream< Char, Traits > &	out,
		rational< T > const &	rat
	)

Output operator.

Definition at line 562 of file rational.hpp.

References rational< T >::numerator().

{
  typename std::basic_ostream<Char, Traits>::sentry sentry{out};
  std::ostringstream stream;
  stream << rat.numerator() << '/' << rat.denominator();
  out << stream.str();
  return out;
}

template<class T >

bool operator<= ( rational< T > const &  a, rational< T > const &  b  )

inline

Less-than-or-equal comparison.

Definition at line 463 of file rational.hpp.

{
  return not (b < a);
}

template<class T >

bool operator<= ( rational< T > const &  a, T const &  b  )

inline

Less-than-or-equal comparison.

Definition at line 470 of file rational.hpp.

{
  return not (b < a);
}

template<class T >

bool operator<= ( T const &  a, rational< T > const &  b  )

inline

Less-than-or-equal comparison.

Definition at line 477 of file rational.hpp.

{
  return not (b < a);
}

template<class T , class U >

bool operator==	(	rational< T > const &	a,
		rational< U > const &	b
	)

Equality comparison.

Definition at line 397 of file rational.hpp.

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

{
  return a.numerator() == b.numerator() and
         a.denominator() == b.denominator();
}

template<class T >

bool operator==	(	rational< T > const &	lhs,
		T	rhs
	)

Equality comparison.

Definition at line 405 of file rational.hpp.

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

{
  return lhs.denominator() == 1 and
         lhs.numerator()   == rhs;
}

template<class T >

bool operator==	(	T	lhs,
		rational< T > const &	rhs
	)

Equality comparison.

Definition at line 413 of file rational.hpp.

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

{
  return rhs.denominator() == 1 and
         rhs.numerator()   == lhs;
}

template<class T >

bool operator> ( rational< T > const &  a, rational< T > const &  b  )

inline

Greater-than comparison.

Definition at line 484 of file rational.hpp.

{
  return b < a;
}

template<class T >

bool operator> ( rational< T > const &  a, T const &  b  )

inline

Greater-than comparison.

Definition at line 491 of file rational.hpp.

{
  return b < a;
}

template<class T >

bool operator> ( T const &  a, rational< T > const &  b  )

inline

Greater-than comparison.

Definition at line 498 of file rational.hpp.

{
  return b < a;
}

template<class T >

bool operator>= ( rational< T > const &  a, rational< T > const &  b  )

inline

Greater-than-or-equal comparison.

Definition at line 505 of file rational.hpp.

{
  return not (b > a);
}

template<class T >

bool operator>= ( rational< T > const &  a, T const &  b  )

inline

Greater-than-or-equal comparison.

Definition at line 512 of file rational.hpp.

{
  return not (b > a);
}

template<class T >

bool operator>= ( T const &  a, rational< T > const &  b  )

inline

Greater-than-or-equal comparison.

Definition at line 519 of file rational.hpp.

{
  return not (b > a);
}

template<class T , class Char , class Traits >

std::basic_istream<Char, Traits>& operator>>	(	std::basic_istream< Char, Traits > &	in,
		rational< T > &	rat
	)

Input operator.

Definition at line 526 of file rational.hpp.

{
  typename std::basic_istream<Char, Traits>::sentry sentry{in, false};
  ioflags flags{in};

  T n{};
  if (not (in >> n))
    // Error reading the numerator.
    return in;

  in >> std::noskipws;
  char sep{};
  if (not (in >> sep))
    // Error reading the separator character.
    return in;
  else if (sep != '/')
  {
    // Push sep back into the input stream, so the next input operation
    // will read it.
    in.unget();
    rat = n;
    return in;
  }
  else
  {
    T d{};
    if (in >> d)
      // Successfully read numerator, separator, and denominator.
      rat = rational<T>{n, d};
  }

  return in;
}