rational< T > Class Template Reference

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

#include <rational.hpp>

List of all members.

Public Types

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

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.
value_type numerator () const
 Return the numerator.
value_type denominator () const
 Return the denominator.
template<class U>
U as () const
 Convert the rational number to another type, especially floating-point.
rational & operator= (value_type)
 Assignment of an integer.
template<class U>
rational & operator= (rational< U > const &rhs)
 Assignment of a rational with a different size.
rational & operator+= (rational const &rhs)
 Addition assignment operator.
rational & operator+= (value_type const &rhs)
 Addition assignment operator.
rational & operator-= (rational const &rhs)
 Subtraction assignment operator.
rational & operator-= (value_type const &rhs)
 Subtraction assignment operator.
rational & operator *= (rational const &rhs)
 Multiplication assignment operator.
rational & operator *= (value_type const &rhs)
 Multiplication assignment operator.
rational & operator/= (rational const &rhs)
 Division assignment operator.
rational & operator/= (value_type const &rhs)
 Division assignment operator.
rational & operator++ ()
 Pre-increment.
rational & operator-- ()
 Pre-decrement.
rational operator++ (int)
 Post-increment.
rational operator-- (int)
 Post-decrement.

Private Member Functions

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

Private Attributes

value_type numerator_
value_type denominator_

Classes

class  zero_denominator
 Exception class if the denominator is ever zero. More...

Detailed Description

template<class T>
class rational< T >

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

Definition at line 16 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 20 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 33 of file rational.hpp.

00033 : numerator_(num), denominator_(1) {}

template<class T>
rational< T >::rational ( value_type  num,
value_type  den 
) [inline]

Construct a rational number

Parameters:
num numerator
den denominator
Exceptions:
zero_denominator if den == 0

Definition at line 106 of file rational.hpp.

References rational< T >::normalize().

00107 : numerator_(num),
00108   denominator_(den == value_type() ? throw zero_denominator("zero denominator") : den)
00109 {
00110   normalize();
00111 }

template<class T>
rational< T >::rational ( double  r  )  [inline]

Initialize the rational number with an approximation of r

Parameters:
r the initial value

Definition at line 114 of file rational.hpp.

00115 : numerator_(static_cast<T>(r / 100000)), denominator_(static_cast<T>(100000))
00116 {}

template<class T>
template<class U>
rational< T >::rational ( rational< U > const &  that  )  [inline]

Copy from a different type of rational.

Definition at line 120 of file rational.hpp.

References rational< T >::reduce().

00121 : numerator_(scale<U>(that.numerator())), denominator_(scale<U>(that.denominator()))
00122 {
00123   reduce();
00124 }

Member Function Documentation

template<class T>
value_type rational< T >::numerator (  )  const [inline]

Return the numerator.

Definition at line 47 of file rational.hpp.

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

00047 { return numerator_; }

template<class T>
value_type rational< T >::denominator (  )  const [inline]

Return the denominator.

Definition at line 49 of file rational.hpp.

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

00049 { return denominator_; }

template<class T>
template<class U>
U rational< T >::as (  )  const [inline]

Convert the rational number to another type, especially floating-point.

Definition at line 52 of file rational.hpp.

00052 { return static_cast<U>(numerator()) / denominator(); }

template<class T>
rational< T > & rational< T >::operator= ( value_type  num  )  [inline]

Assignment of an integer.

Definition at line 158 of file rational.hpp.

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

00159 {
00160   numerator_ = num;
00161   denominator_ = value_type(1);
00162   return *this;
00163 }

template<class T>
template<class U>
rational< T > & rational< T >::operator= ( rational< U > const &  rhs  )  [inline]

Assignment of a rational with a different size.

Definition at line 167 of file rational.hpp.

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

00168 {
00169   numerator_ = scale<U>(rhs.numerator());
00170   denominator_ = scale<U>(rhs.denominator());
00171   reduce();
00172   return *this;
00173 }

template<class T>
rational< T > & rational< T >::operator+= ( rational< T > const &  rhs  )  [inline]

Addition assignment operator.

Definition at line 176 of file rational.hpp.

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

00177 {
00178   numerator_ = numerator() * rhs.denominator() + rhs.numerator() * denominator();
00179   denominator_ *= rhs.denominator();
00180   reduce();
00181   return *this;
00182 }

template<class T>
rational< T > & rational< T >::operator+= ( value_type const &  rhs  )  [inline]

Addition assignment operator.

Definition at line 185 of file rational.hpp.

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

00186 {
00187   numerator_ = numerator() + rhs * denominator();
00188   reduce();
00189   return *this;
00190 }

template<class T>
rational< T > & rational< T >::operator-= ( rational< T > const &  rhs  )  [inline]

Subtraction assignment operator.

Definition at line 193 of file rational.hpp.

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

00194 {
00195   numerator_ = numerator() * rhs.denominator() - rhs.numerator() * denominator();
00196   denominator_ *= rhs.denominator();
00197   reduce();
00198   return *this;
00199 }

template<class T>
rational< T > & rational< T >::operator-= ( value_type const &  rhs  )  [inline]

Subtraction assignment operator.

Definition at line 202 of file rational.hpp.

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

00203 {
00204   numerator_ = numerator() - rhs * denominator();
00205   reduce();
00206   return *this;
00207 }

template<class T>
rational< T > & rational< T >::operator *= ( rational< T > const &  rhs  )  [inline]

Multiplication assignment operator.

Definition at line 210 of file rational.hpp.

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

00211 {
00212   numerator_ *= rhs.numerator();
00213   denominator_ *= rhs.denominator();
00214   reduce();
00215   return *this;
00216 }

template<class T>
rational< T > & rational< T >::operator *= ( value_type const &  rhs  )  [inline]

Multiplication assignment operator.

Definition at line 219 of file rational.hpp.

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

00220 {
00221   numerator_ *= rhs;
00222   reduce();
00223   return *this;
00224 }

template<class T>
rational< T > & rational< T >::operator/= ( rational< T > const &  rhs  )  [inline]

Division assignment operator.

Definition at line 227 of file rational.hpp.

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

00228 {
00229   if (rhs.numerator() == value_type())
00230     throw zero_denominator("divide by zero");
00231   numerator_ *= rhs.denominator();
00232   denominator_ *= rhs.numerator();
00233   normalize();
00234   return *this;
00235 }

template<class T>
rational< T > & rational< T >::operator/= ( value_type const &  rhs  )  [inline]

Division assignment operator.

Definition at line 238 of file rational.hpp.

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

00239 {
00240   if (rhs == value_type())
00241     throw zero_denominator("divide by zero");
00242   denominator_ *= rhs;
00243   normalize();
00244   return *this;
00245 }

template<class T>
rational< T > & rational< T >::operator++ (  )  [inline]

Pre-increment.

Definition at line 248 of file rational.hpp.

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

00249 {
00250   numerator_ += denominator();
00251   return *this;
00252 }

template<class T>
rational< T > & rational< T >::operator-- (  )  [inline]

Pre-decrement.

Definition at line 263 of file rational.hpp.

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

00264 {
00265   numerator_ -= denominator();
00266   return *this;
00267 }

template<class T>
rational< T > rational< T >::operator++ ( int   )  [inline]

Post-increment.

Definition at line 255 of file rational.hpp.

00256 {
00257   rational result(*this);
00258   ++*this;
00259   return result;
00260 }

template<class T>
rational< T > rational< T >::operator-- ( int   )  [inline]

Post-decrement.

Definition at line 270 of file rational.hpp.

00271 {
00272   rational result(*this);
00273   --*this;
00274   return result;
00275 }

template<class T>
void rational< T >::reduce (  )  [inline, private]

Reduce the numerator and denominator by their GCD.

Definition at line 148 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().

00149 {
00150   value_type div(gcd(numerator(), denominator()));
00151   if (div == value_type())
00152     throw zero_denominator("zero denominator");
00153   numerator_ /= div;
00154   denominator_ /= div;
00155 }

template<class T>
void rational< T >::normalize (  )  [inline, private]

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

Definition at line 137 of file rational.hpp.

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

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

00138 {
00139   if (denominator_ < value_type())
00140   {
00141     denominator_ = -denominator_;
00142     numerator_ = -numerator_;
00143   }
00144   reduce();
00145 }

template<class T>
template<class U>
T rational< T >::scale ( U  value  )  [inline, private]

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

Definition at line 128 of file rational.hpp.

00129 {
00130   if (std::numeric_limits<T>::digits >= std::numeric_limits<U>::digits)
00131     return T(value);
00132   else
00133     return T(value >> (std::numeric_limits<U>::digits - std::numeric_limits<T>::digits));
00134 }

Member Data Documentation

template<class T>
value_type rational< T >::numerator_ [private]

Definition at line 101 of file rational.hpp.

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

template<class T>
value_type rational< T >::denominator_ [private]

Definition at line 102 of file rational.hpp.

Referenced by rational< long >::denominator(), rational< T >::normalize(), 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:
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