Rational

NEGATIVE_INFINITY

public static final Rational NEGATIVE_INFINITY

Constant for the negative infinity value of the Rational type.

Equivalent to constructing a new rational with a negative numerator and a denominator equal to 0.

NaN

public static final Rational NaN

Constant for the Not-a-Number (NaN) value of the Rational type.

A NaN value is considered to be equal to itself (that is NaN.equals(NaN) will return true; it is always greater than any non-NaN value (that is NaN.compareTo(notNaN) will return a number greater than 0).

Equivalent to constructing a new rational with both the numerator and denominator equal to 0.

POSITIVE_INFINITY

public static final Rational POSITIVE_INFINITY

Constant for the positive infinity value of the Rational type.

Equivalent to constructing a new rational with a positive numerator and a denominator equal to 0.

ZERO

public static final Rational ZERO

Constant for the zero value of the Rational type.

Equivalent to constructing a new rational with a numerator equal to 0 and any non-zero denominator.

Rational

public Rational (int numerator, 
                int denominator)

Create a Rational with a given numerator and denominator.

The signs of the numerator and the denominator may be flipped such that the denominator is always positive. Both the numerator and denominator will be converted to their reduced forms (see equals(Object) for more details).

For example,

• a rational of 2/4 will be reduced to 1/2.
• a rational of 1/-1 will be flipped to -1/1
• a rational of 5/0 will be reduced to 1/0
• a rational of 0/5 will be reduced to 0/1

compareTo

public int compareTo (Rational another)

Compare this rational to the specified rational to determine their natural order.

NaN is considered to be equal to itself and greater than all other Rational values. Otherwise, if the objects are not equal, then the following rules apply:

• Positive infinity is greater than any other finite number (or negative infinity)
• Negative infinity is less than any other finite number (or positive infinity)
• The finite number represented by this rational is checked numerically against the other finite number by converting both rationals to a common denominator multiple and comparing their numerators.

doubleValue

public double doubleValue ()

Returns the value of the specified number as a double.

The double is calculated by converting both the numerator and denominator to a double; then returning the result of dividing the numerator by the denominator.

equals

public boolean equals (Object obj)

Compare this Rational to another object and see if they are equal.

A Rational object can only be equal to another Rational object (comparing against any other type will return false).

A Rational object is considered equal to another Rational object if and only if one of the following holds:

• Both are NaN
• Both are infinities of the same sign
• Both have the same numerator and denominator in their reduced form

A reduced form of a Rational is calculated by dividing both the numerator and the denominator by their greatest common divisor.

(new Rational(1, 2)).equals(new Rational(1, 2)) == true   // trivially true
 (new Rational(2, 3)).equals(new Rational(1, 2)) == false  // trivially false
 (new Rational(1, 2)).equals(new Rational(2, 4)) == true   // true after reduction
 (new Rational(0, 0)).equals(new Rational(0, 0)) == true   // NaN.equals(NaN)
 (new Rational(1, 0)).equals(new Rational(5, 0)) == true   // both are +infinity
 (new Rational(1, 0)).equals(new Rational(-1, 0)) == false // +infinity != -infinity
 

floatValue

public float floatValue ()

Returns the value of the specified number as a float.

The float is calculated by converting both the numerator and denominator to a float; then returning the result of dividing the numerator by the denominator.

getDenominator

public int getDenominator ()

Gets the denominator of the rational

The denominator may return 0, in which case the rational may represent positive infinity (if the numerator was positive), negative infinity (if the numerator was negative), or NaN (if the numerator was 0).

The denominator will always return 1 if the numerator is 0.

getNumerator

public int getNumerator ()

Gets the numerator of the rational.

The numerator will always return 1 if this rational represents infinity (that is, the denominator is 0).

hashCode

public int hashCode ()

Returns a hash code value for the object. This method is supported for the benefit of hash tables such as those provided by HashMap.

The general contract of hashCode is:

• Whenever it is invoked on the same object more than once during an execution of a Java application, the hashCode method must consistently return the same integer, provided no information used in equals comparisons on the object is modified. This integer need not remain consistent from one execution of an application to another execution of the same application.
• If two objects are equal according to the equals method, then calling the hashCode method on each of the two objects must produce the same integer result.
• It is not required that if two objects are unequal according to the equals method, then calling the hashCode method on each of the two objects must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal objects may improve the performance of hash tables.

intValue

public int intValue ()

Returns the value of the specified number as a int.

Finite rationals are converted to an int value by dividing the numerator by the denominator; conversion for non-finite values happens identically to casting a floating point value to an int, in particular:

• Positive infinity saturates to the largest maximum integer Integer.MAX_VALUE
• Negative infinity saturates to the smallest maximum integer Integer.MIN_VALUE
• Not-A-Number (NaN) returns 0.

isFinite

public boolean isFinite ()

Indicates whether this rational represents a finite value.

A finite value occurs when the denominator is not 0; in other words the rational is neither infinity or NaN.

isInfinite

public boolean isInfinite ()

Indicates whether this rational represents an infinite value.

An infinite value occurs when the denominator is 0 (but the numerator is not).

isNaN

public boolean isNaN ()

Indicates whether this rational is a Not-a-Number (NaN) value.

A NaN value occurs when both the numerator and the denominator are 0.

isZero

public boolean isZero ()

Indicates whether this rational represents a zero value.

A zero value is a finite rational with a numerator of 0.

longValue

public long longValue ()

Returns the value of the specified number as a long.

Finite rationals are converted to an long value by dividing the numerator by the denominator; conversion for non-finite values happens identically to casting a floating point value to a long, in particular:

• Positive infinity saturates to the largest maximum long Long.MAX_VALUE
• Negative infinity saturates to the smallest maximum long Long.MIN_VALUE
• Not-A-Number (NaN) returns 0.

parseRational

public static Rational parseRational (String string)

Parses the specified string as a rational value.

The ASCII characters \u003a (':') and \u002f ('/') are recognized as separators between the numerator and denumerator.

For any Rational r: Rational.parseRational(r.toString()).equals(r). However, the method also handles rational numbers expressed in the following forms:

"num/den" or "num:den" => new Rational(num, den);, where num and den are string integers potentially containing a sign, such as "-10", "+7" or "5".

Rational.parseRational("3:+6").equals(new Rational(1, 2)) == true
 Rational.parseRational("-3/-6").equals(new Rational(1, 2)) == true
 Rational.parseRational("4.56") => throws NumberFormatException
 

shortValue

public short shortValue ()

Returns the value of the specified number as a short.

Finite rationals are converted to a short value identically to intValue(); the int result is then truncated to a short before returning the value.

toString

public String toString ()

Return a string representation of this rational, e.g. "1/2".

The following rules of conversion apply:

• NaN values will return "NaN"
• Positive infinity values will return "Infinity"
• Negative infinity values will return "-Infinity"
• All other values will return "numerator/denominator" where numerator and denominator are substituted with the appropriate numerator and denominator values.