edu.rit.numeric
Class BigRational

java.lang.Object
  java.lang.Number
      edu.rit.numeric.BigRational

All Implemented Interfaces:

Serializable, Comparable<BigRational>

public class BigRational
extends Number
implements Comparable<BigRational>

Class BigRational provides an arbitrary precision rational number. An arbitrary precision rational number is the ratio of two arbitrary precision integers (type java.math.BigInteger). Operations are provided for exact arithmetic with rational numbers.

A rational number is said to be normalized if GCD(numerator,denominator) = 1. The methods below do not automatically normalize the rational number. Thus, the numerator and denominator tend to get larger and larger as operations are performed on the rational number. To reduce the numerator and denominator to lowest terms again, call the normalize() method. It is up to you to decide whether to normalize the rational number after each operation, or after a series of operations.

Class BigRational provides the equals() and hashCode() methods, and BigRational objects can be used as keys in hashed data structures. However, BigRational objects are mutable. If a BigRational object is used as a hash key, be sure not to change its value.

Class BigRational is not multiple thread safe.

See Also:

Serialized Form

Constructor Summary

BigRational()
Construct a new rational number.

BigRational(BigInteger x)
Construct a new rational number.

BigRational(BigInteger n, BigInteger d)
Construct a new rational number.

BigRational(BigRational x)
Construct a new rational number.

BigRational(long x)
Construct a new rational number.

BigRational(long n, long d)
Construct a new rational number.

BigRational(String s)
Construct a new rational number.

Method Summary

BigRational	abs() Set this rational number to the absolute value of itself.
BigRational	add(BigRational x) Set this rational number to the sum of itself and the given number.
BigRational	assign(BigInteger x) Set this rational number to the given number.
BigRational	assign(BigInteger n, BigInteger d) Set this rational number to the given fraction.
BigRational	assign(BigRational x) Set this rational number to the given number.
BigRational	assign(long x) Set this rational number to the given number.
BigRational	assign(long n, long d) Set this rational number to the given fraction.
BigRational	assign(String s) Set this rational number to the value parsed from the given string.
int	compareTo(BigRational x) Compare this rational number to the given rational number.
BigRational	decr() Decrement this rational number.
BigInteger	denominator() Returns this rational number's denominator.
BigRational	div(BigRational x) Set this rational number to the quotient of itself and the given number.
double	doubleValue() Converts this rational number to a double precision floating point number.
boolean	equals(Object obj) Determine if this rational number equals the given object.
float	floatValue() Converts this rational number to a single precision floating point number.
BigRational	fracPart() Set this rational number to the fractional part of itself.
int	hashCode() Returns a hash code for this rational number.
BigRational	incr() Increment this rational number.
BigRational	intPart() Set this rational number to the integer part of itself.
int	intValue() Converts this rational number to an integer.
long	longValue() Converts this rational number to a long integer.
BigRational	max(BigRational x) Set this rational number to the larger of itself and the given number.
BigRational	min(BigRational x) Set this rational number to the smaller of itself and the given number.
BigRational	mul(BigRational x) Set this rational number to the product of itself and the given number.
BigRational	negate() Set this rational number to the negative of itself.
BigRational	normalize() Normalize this rational number.
BigInteger	numerator() Returns this rational number's numerator.
BigRational	recip() Set this rational number to the reciprocal of itself.
BigRational	rem(BigRational x) Set this rational number to the remainder when divided by the given number.
BigRational	sub(BigRational x) Set this rational number to the difference of itself and the given number.
String	toString() Returns a string version of this rational number.

Methods inherited from class java.lang.Number

byteValue, shortValue

Methods inherited from class java.lang.Object

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

Constructor Detail

BigRational

public BigRational()

Construct a new rational number. Its value is 0.

BigRational

public BigRational(long x)

Construct a new rational number. Its value is x.

Parameters:

x - Long integer.

BigRational

public BigRational(long n,
                   long d)

Construct a new rational number. Its value is n/d.

Parameters:

n - Numerator.

d - Denominator.

Throws:

ArithmeticException - (unchecked exception) Thrown if d is 0.

BigRational

public BigRational(BigInteger x)

Construct a new rational number. Its value is x.

Parameters:

x - Big integer.

BigRational

public BigRational(BigInteger n,
                   BigInteger d)

Construct a new rational number. Its value is n/d.

Parameters:

n - Numerator.

d - Denominator.

Throws:

ArithmeticException - (unchecked exception) Thrown if d is 0.

BigRational

public BigRational(BigRational x)

Construct a new rational number. Its value is x.

Parameters:

x - Rational number.

BigRational

public BigRational(String s)

Construct a new rational number. Its value comes from the string s. The string must obey this syntax: optional minus sign (-), numerator (decimal integer), slash (/), denominator (decimal integer). The slash-and-denominator is optional. If present, the denominator must be greater than 0. There is no whitespace within the string.

Parameters:

s - String.

Throws:

NumberFormatException - (unchecked exception) Thrown if s cannot be parsed into a rational number.

Method Detail

numerator

public BigInteger numerator()

Returns this rational number's numerator.

Returns:

Numerator.

denominator

public BigInteger denominator()

Returns this rational number's denominator.

Returns:

Denominator.

assign

public BigRational assign(long x)

Set this rational number to the given number.

Parameters:

x - Long integer.

Returns:

This rational number, with its value set to x.

assign

public BigRational assign(long n,
                          long d)

Set this rational number to the given fraction.

Parameters:

n - Numerator.

d - Denominator.

Returns:

This rational number, with its value set to n/d.

Throws:

ArithmeticException - (unchecked exception) Thrown if d is 0.

assign

public BigRational assign(BigInteger x)

Set this rational number to the given number.

Parameters:

x - Big integer.

Returns:

This rational number, with its value set to x.

assign

public BigRational assign(BigInteger n,
                          BigInteger d)

Set this rational number to the given fraction.

Parameters:

n - Numerator.

d - Denominator.

Returns:

This rational number, with its value set to n/d.

Throws:

ArithmeticException - (unchecked exception) Thrown if d is 0.

assign

public BigRational assign(BigRational x)

Set this rational number to the given number.

Parameters:

x - Rational number.

Returns:

This rational number, with its value set to x.

assign

public BigRational assign(String s)

Set this rational number to the value parsed from the given string. The string must obey this syntax: optional minus sign (-), numerator (decimal integer), slash (/), denominator (decimal integer). The slash-and-denominator is optional. If present, the denominator must be greater than 0. There is no whitespace within the string.

Parameters:

s - String.

Returns:

This rational number, with its value set to s.

Throws:

NumberFormatException - (unchecked exception) Thrown if s cannot be parsed into a rational number.

intPart

public BigRational intPart()

Set this rational number to the integer part of itself.

Returns:

This rational number, with its value set to int(this).

fracPart

public BigRational fracPart()

Set this rational number to the fractional part of itself.

Returns:

This rational number, with its value set to frac(this).

add

public BigRational add(BigRational x)

Set this rational number to the sum of itself and the given number.

Parameters:

x - Rational number.

Returns:

This rational number, with its value set to this+x.

sub

public BigRational sub(BigRational x)

Set this rational number to the difference of itself and the given number.

Parameters:

x - Rational number.

Returns:

This rational number, with its value set to this-x.

mul

public BigRational mul(BigRational x)

Set this rational number to the product of itself and the given number.

Parameters:

x - Rational number.

Returns:

This rational number, with its value set to this*x.

div

public BigRational div(BigRational x)

Set this rational number to the quotient of itself and the given number.

Parameters:

x - Rational number.

Returns:

This rational number, with its value set to this/x.

Throws:

ArithmeticException - (unchecked exception) Thrown if x is 0.

rem

public BigRational rem(BigRational x)

Set this rational number to the remainder when divided by the given number.

Parameters:

x - Rational number.

Returns:

This rational number, with its value set to frac(this/x)*x.

Throws:

ArithmeticException - (unchecked exception) Thrown if x is 0.

incr

public BigRational incr()

Increment this rational number.

Returns:

This rational number, with its value set to this+1.

decr

public BigRational decr()

Decrement this rational number.

Returns:

This rational number, with its value set to this-1.

abs

public BigRational abs()

Set this rational number to the absolute value of itself.

Returns:

This rational number, with its value set to abs(this).

negate

public BigRational negate()

Set this rational number to the negative of itself.

Returns:

This rational number, with its value set to -this.

recip

public BigRational recip()

Set this rational number to the reciprocal of itself.

Returns:

This rational number, with its value set to 1/this.

Throws:

ArithmeticException - (unchecked exception) Thrown if this rational number is 0.

min

public BigRational min(BigRational x)

Set this rational number to the smaller of itself and the given number.

Parameters:

x - Rational number.

Returns:

This rational number, with its value set to min(this,x).

max

public BigRational max(BigRational x)

Set this rational number to the larger of itself and the given number.

Parameters:

x - Rational number.

Returns:

This rational number, with its value set to max(this,x).

normalize

public BigRational normalize()

Normalize this rational number. Afterwards, the denominator is greater than or equal to 1, and the denominator does not divide the numerator; in other words, GCD(numerator,denominator) = 1.

Returns:

This rational number, normalized.

intValue

public int intValue()

Converts this rational number to an integer.

Specified by:

intValue in class Number

Returns:

Integer value of this rational number.

longValue

public long longValue()

Converts this rational number to a long integer.

Specified by:

longValue in class Number

Returns:

Long integer value of this rational number.

floatValue

public float floatValue()

Converts this rational number to a single precision floating point number.

Specified by:

floatValue in class Number

Returns:

Single precision floating point value of this rational number.

doubleValue

public double doubleValue()

Converts this rational number to a double precision floating point number.

Specified by:

doubleValue in class Number

Returns:

Double precision floating point value of this rational number.

compareTo

public int compareTo(BigRational x)

Compare this rational number to the given rational number.

Specified by:

compareTo in interface Comparable<BigRational>

Parameters:

x - Rational number to compare.

Returns:

A number less than, equal to, or greater than 0 if this rational number is less than, equal to, or greater than x, respectively.

equals

public boolean equals(Object obj)

Determine if this rational number equals the given object.

Note: Class BigRational provides the equals() and hashCode() methods, and BigRational objects can be used as keys in hashed data structures. However, BigRational objects are mutable. If a BigRational object is used as a hash key, be sure not to change its value.

Note: Two rational numbers are equal only if their numerators and denominators are equal. Thus, it is possible for equals() to return false even if the two rational numbers have the same numerical value. To ensure that equals() will return true if the two rational numbers have the same numerical value, normalize the two rational numbers first.

Overrides:

equals in class Object

Parameters:

obj - Object to compare.

Returns:

True if this rational number equals obj, false otherwise.

hashCode

public int hashCode()

Returns a hash code for this rational number.

Note: Class BigRational provides the equals() and hashCode() methods, and BigRational objects can be used as keys in hashed data structures. However, BigRational objects are mutable. If a BigRational object is used as a hash key, be sure not to change its value.

Note: Two rational numbers have the same hash code only if their numerators and denominators are equal. Thus, it is possible for hashCode() to return different values even if the two rational numbers have the same numerical value. To ensure that hashCode() will return the same value if the two rational numbers have the same numerical value, normalize the two rational numbers first.

Overrides:

hashCode in class Object

Returns:

Hash code.

toString

public String toString()

Returns a string version of this rational number. If this rational number's denominator is 1, the string is in the form "<numer>", otherwise the string is in the form "<numer>/<denom>". The negative sign, if any, is attached to the numerator.

Note: The toString() method yields the numerator and denominator as they are, without normalizing this rational number.

Overrides:

toString in class Object