com.drew.lang
Class Rational

java.lang.Object
  java.lang.Number
      com.drew.lang.Rational

All Implemented Interfaces:

Serializable

public class Rational
extends Number
implements Serializable

Immutable class for holding a rational number without loss of precision. Provides a familiar representation via toString() in form numerator/denominator.

Author:

Drew Noakes http://drewnoakes.com

See Also:

Serialized Form

Field Summary

private int	denominator Holds the denominator.
private int	maxSimplificationCalculations
private int	numerator Holds the numerator.

Constructor Summary

Rational(int numerator, int denominator)
Creates a new instance of Rational.

Method Summary

byte	byteValue() Returns the value of the specified number as a byte.
double	doubleValue() Returns the value of the specified number as a double.
boolean	equals(Object obj) Compares two Rational instances, returning true if they are mathematically equivalent.
float	floatValue() Returns the value of the specified number as a float.
int	getDenominator() Returns the denominator.
int	getNumerator() Returns the numerator.
Rational	getReciprocal() Returns the reciprocal value of this obejct as a new Rational.
Rational	getSimplifiedInstance() Simplifies the Rational number.
int	intValue() Returns the value of the specified number as an int.
boolean	isInteger() Checks if this rational number is an Integer, either positive or negative.
long	longValue() Returns the value of the specified number as a long.
short	shortValue() Returns the value of the specified number as a short.
private boolean	tooComplexForSimplification() Decides whether a brute-force simplification calculation should be avoided by comparing the maximum number of possible calculations with some threshold.
String	toSimpleString(boolean allowDecimal) Returns the simplest represenation of this Rational's value possible.
String	toString() Returns a string representation of the object of form numerator/denominator.

Methods inherited from class java.lang.Object

clone, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Field Detail

numerator

private final int numerator

Holds the numerator.

denominator

private final int denominator

Holds the denominator.

maxSimplificationCalculations

private int maxSimplificationCalculations

Constructor Detail

Rational

public Rational(int numerator,
                int denominator)

Creates a new instance of Rational. Rational objects are immutable, so once you've set your numerator and denominator values here, you're stuck with them!

Method Detail

doubleValue

public double doubleValue()

Returns the value of the specified number as a double. This may involve rounding.

Specified by:

doubleValue in class Number

Returns:

the numeric value represented by this object after conversion to type double.

floatValue

public float floatValue()

Returns the value of the specified number as a float. This may involve rounding.

Specified by:

floatValue in class Number

Returns:

the numeric value represented by this object after conversion to type float.

byteValue

public final byte byteValue()

Returns the value of the specified number as a byte. This may involve rounding or truncation. This implementation simply casts the result of doubleValue() to byte.

Overrides:

byteValue in class Number

Returns:

the numeric value represented by this object after conversion to type byte.

intValue

public final int intValue()

Returns the value of the specified number as an int. This may involve rounding or truncation. This implementation simply casts the result of doubleValue() to int.

Specified by:

intValue in class Number

Returns:

the numeric value represented by this object after conversion to type int.

longValue

public final long longValue()

Returns the value of the specified number as a long. This may involve rounding or truncation. This implementation simply casts the result of doubleValue() to long.

Specified by:

longValue in class Number

Returns:

the numeric value represented by this object after conversion to type long.

shortValue

public final short shortValue()

Returns the value of the specified number as a short. This may involve rounding or truncation. This implementation simply casts the result of doubleValue() to short.

Overrides:

shortValue in class Number

Returns:

the numeric value represented by this object after conversion to type short.

getDenominator

public final int getDenominator()

Returns the denominator.

getNumerator

public final int getNumerator()

Returns the numerator.

getReciprocal

public Rational getReciprocal()

Returns the reciprocal value of this obejct as a new Rational.

Returns:

the reciprocal in a new object

isInteger

public boolean isInteger()

Checks if this rational number is an Integer, either positive or negative.

toString

public String toString()

Returns a string representation of the object of form numerator/denominator.

Overrides:

toString in class Object

Returns:

a string representation of the object.

toSimpleString

public String toSimpleString(boolean allowDecimal)

Returns the simplest represenation of this Rational's value possible.

tooComplexForSimplification

private boolean tooComplexForSimplification()

Decides whether a brute-force simplification calculation should be avoided by comparing the maximum number of possible calculations with some threshold.

Returns:

true if the simplification should be performed, otherwise false

equals

public boolean equals(Object obj)

Compares two Rational instances, returning true if they are mathematically equivalent.

Overrides:

equals in class Object

Parameters:

obj - the Rational to compare this instance to.

Returns:

true if instances are mathematically equivalent, otherwise false. Will also return false if obj is not an instance of Rational.

getSimplifiedInstance

public Rational getSimplifiedInstance()

Simplifies the Rational number.

Prime number series: 1, 2, 3, 5, 7, 9, 11, 13, 17

To reduce a rational, need to see if both numerator and denominator are divisible by a common factor. Using the prime number series in ascending order guarantees the minimun number of checks required.

However, generating the prime number series seems to be a hefty task. Perhaps it's simpler to check if both d & n are divisible by all numbers from 2 -> (Math.min(denominator, numerator) / 2). In doing this, one can check for 2 and 5 once, then ignore all even numbers, and all numbers ending in 0 or 5. This leaves four numbers from every ten to check.

Therefore, the max number of pairs of modulus divisions required will be:

    4   Math.min(denominator, numerator) - 1
   -- * ------------------------------------ + 2
   10                    2

   Math.min(denominator, numerator) - 1
 = ------------------------------------ + 2
                  5
 

Returns:

a simplified instance, or if the Rational could not be simpliffied, returns itself (unchanged)