# Class Fraction

Object
Number
Fraction

All Implemented Interfaces:
  `Serializable`, `Comparable<Fraction>`

public final class Fraction extends Number implements Comparable<Fraction>, Serializable
A value class for rational numbers. `Fraction` objects are represented by a numerator and a denominator stored at 32 bits integers. Fractions can be simplified. All `Fraction` instances are immutable and thus inherently thread-safe.

Since:
  0.8
See Also:
  - Serialized Form

- ## Field Summary

  Fields
  Modifier and Type
  Field
  Description
  `final int`
  `denominator`
  The b term in the a/b fraction.
  `final int`
  `numerator`
  The a term in the a/b fraction.

- ## Constructor Summary

  Constructors
  Constructor
  Description
  `Fraction(int numerator, int denominator)`
  Creates a new fraction.
  `Fraction(String s)`
  Creates a new fraction from the given text.

- ## Method Summary

  Modifier and Type
  Method
  Description
  `Fraction`
  `add(Fraction other)`
  Returns the simplified result of adding the given fraction to this fraction.
  `int`
  `ceil()`
  Returns this fraction rounded toward positive infinity.
  `int`
  `compareTo(Fraction other)`
  Compares this fraction with the given one for order.
  `Fraction`
  `divide(Fraction other)`
  Returns the simplified result of dividing this fraction by the given fraction.
  `double`
  `doubleValue()`
  Returns the fraction as a double-precision floating point number.
  `boolean`
  `equals(Object other)`
  Compares this fraction with the given object for equality.
  `float`
  `floatValue()`
  Returns the fraction as a single-precision floating point number.
  `int`
  `floor()`
  Returns this fraction rounded toward negative infinity.
  `int`
  `hashCode()`
  Returns a hash code value for this fraction.
  `int`
  `intValue()`
  Returns this fraction rounded toward zero.
  `Fraction`
  `inverse()`
  Returns the inverse value of this fraction.
  `boolean`
  `isNaN()`
  Returns `true` if the numerator and denominator are both zero.
  `long`
  `longValue()`
  Returns this fraction rounded toward zero.
  `Fraction`
  `multiply(Fraction other)`
  Returns the simplified result of multiplying the given fraction with this fraction.
  `Fraction`
  `negate()`
  Returns the negative value of this fraction.
  `int`
  `round()`
  Returns this fraction rounded toward nearest integer.
  `int`
  `signum()`
  Returns the sign of this fraction.
  `Fraction`
  `simplify()`
  Returns a fraction equivalent to `this` but represented by the smallest possible numerator and denominator values.
  `Fraction`
  `subtract(Fraction other)`
  Returns the simplified result of subtracting the given fraction from this fraction.
  `String`
  `toString()`
  Returns a string representation of this fraction.
  `Fraction`
  `unique()`
  Returns a unique fraction instance equals to `this`.
  `static Fraction`
  `valueOf(double value)`
  Converts the given IEEE 754 double-precision value to a fraction.
  `static Fraction`
  `valueOf(long numerator, long denominator)`
  Returns the given fraction after simplification.

  ### Methods inherited from class Number

  `byteValue, shortValue`

  ### Methods inherited from class Object

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

- ## Field Details

  - ### numerator

    public final int numerator
    The a term in the a/b fraction. Can be positive, negative or zero.
    See Also:
      - `doubleValue()`

  - ### denominator

    public final int denominator
    The b term in the a/b fraction. Can be positive, negative or zero. If zero, then the fraction floating point value will be positive infinity, negative infinity or NaN depending on the numerator value.
    See Also:
      - `doubleValue()`

- ## Constructor Details

  - ### Fraction

    public Fraction(int numerator, int denominator)
    Creates a new fraction. This constructor stores the fraction exactly as specified; it does not simplify it. The fraction can be simplified after construction by a call to `simplify()`.
    Parameters:
      `numerator` - the a term in the a/b fraction.
      `denominator` - the b term in the a/b fraction.

  - ### Fraction

    public Fraction(String s) throws NumberFormatException
    Creates a new fraction from the given text. This constructor is the converse of `toString()` method. It can parse single numbers like "3", fractions like "2/3", Unicode characters like "⅔" and infinity symbols "∞" and "−∞". The given text shall not contain spaces.
    Parameters:
      `s` - the text to parse.
    Throws:
      `NumberFormatException` - if the given text cannot be parsed.
    Since:
      1.0

- ## Method Details

  - ### valueOf

    public static Fraction valueOf(long numerator, long denominator)
    Returns the given fraction after simplification. If the numerator or denominator is still too large for 32 bit integer after simplification, then an `ArithmeticException` is thrown.
    Parameters:
      `numerator` - numerator of the fraction to return.
      `denominator` - denominator of the fraction to return.
    Returns:
      the simplified fraction.
    Throws:
      `ArithmeticException` - if the numerator and denominator cannot be represented by 32 bit integers.
    Since:
      1.4

  - ### valueOf

    public static Fraction valueOf(double value)
    Converts the given IEEE 754 double-precision value to a fraction. If successful, this method returns a fraction such as `doubleValue()` is equal to the given value in the sense of `Double​.equals(Object)`: infinities, positive and negative zeros are preserved, but various NaN values are collapsed to a single NaN value.

    This method accepts only values between -2147483648 and 2147483647 inclusive, i.e. values in the range of 32-bits integers. If the given value has fraction digits, then the validity range will be smaller depending on the denominator required for representing that value.

    #### Design note

    This method does not return approximated values because it is difficult to choose which fraction is best. For example, choosing an approximated fraction for π value is quite arbitrary, and searching the fraction closer than any other fraction representable by this class is computationally expensive. Even with common fractions, the algorithm currently implemented in this class can detect that 1.6666666666666667 is equal to 5⁄3 but cannot detect easily that 1.66666666666666 (same number with two decimal digits dropped) is close to 5⁄3.
    Parameters:
      `value` - the double-precision value to convert to a fraction.
    Returns:
      a fraction such as `doubleValue()` is equal to the given value.
    Throws:
      `IllegalArgumentException` - if the given value cannot be converted to a fraction.
    Since:
      1.0

  - ### unique

    public Fraction unique()
    Returns a unique fraction instance equals to `this`. If this method has been invoked previously on another `Fraction` with the same value as `this`, then that previous instance is returned (provided that it has not yet been garbage collected). Otherwise this method adds this fraction to the pool of fractions that may be returned in next `unique()` invocations, then returns `this`.

    This method is useful for saving memory when a potentially large number of `Fraction` instances will be kept for a long time and many instances are likely to have the same values. It is usually not worth to invoke this method for short-lived instances.

    Returns:
      a unique instance of a fraction equals to `this`.

  - ### simplify

    public Fraction simplify()
    Returns a fraction equivalent to `this` but represented by the smallest possible numerator and denominator values. If this fraction cannot be simplified, then this method returns `this`.
    Returns:
      the simplest fraction equivalent to this fraction.

  - ### inverse

    public Fraction inverse()
    Returns the inverse value of this fraction. This method does not simplify the fraction.
    Returns:
      the result of `1/this`.
    Throws:
      `ArithmeticException` - if the result overflows.
    Since:
      1.4
    See Also:
      - `divide(Fraction)`

  - ### negate

    public Fraction negate()
    Returns the negative value of this fraction. This method does not simplify the fraction.
    Returns:
      the result of `-this`.
    Throws:
      `ArithmeticException` - if the result overflows.
    See Also:
      - `subtract(Fraction)`

  - ### add

    public Fraction add(Fraction other)
    Returns the simplified result of adding the given fraction to this fraction.
    Parameters:
      `other` - the fraction to add to this fraction.
    Returns:
      the simplified result of `this` + `other`.
    Throws:
      `ArithmeticException` - if the result overflows.

  - ### subtract

    public Fraction subtract(Fraction other)
    Returns the simplified result of subtracting the given fraction from this fraction.
    Parameters:
      `other` - the fraction to subtract from this fraction.
    Returns:
      the simplified result of `this` - `other`.
    Throws:
      `ArithmeticException` - if the result overflows.
    See Also:
      - `negate()`

  - ### multiply

    public Fraction multiply(Fraction other)
    Returns the simplified result of multiplying the given fraction with this fraction.
    Parameters:
      `other` - the fraction to multiply with this fraction.
    Returns:
      the simplified result of `this` × `other`.
    Throws:
      `ArithmeticException` - if the result overflows.

  - ### divide

    public Fraction divide(Fraction other)
    Returns the simplified result of dividing this fraction by the given fraction.
    Parameters:
      `other` - the fraction by which to divide this fraction.
    Returns:
      the simplified result of `this` ∕ `other`.
    Throws:
      `ArithmeticException` - if the result overflows.
    See Also:
      - `inverse()`

  - ### round

    public int round()
    Returns this fraction rounded toward nearest integer. If the result is located at equal distance from the two nearest integers, then rounds to the even one.
    Returns:
      `numerator` / `denominator` rounded toward nearest integer.

  - ### floor

    public int floor()
    Returns this fraction rounded toward negative infinity. This is different from the default operation on primitive types, which rounds toward zero.

    Tip: if the numerator and the denominator are both positive or both negative, then the result is positive and identical to `numerator / denominator`.

    Returns:
      `numerator` / `denominator` rounded toward negative infinity.

  - ### ceil

    public int ceil()
    Returns this fraction rounded toward positive infinity. This is different from the default operation on primitive types, which rounds toward zero.
    Returns:
      `numerator` / `denominator` rounded toward positive infinity.

  - ### doubleValue

    public double doubleValue()
    Returns the fraction as a double-precision floating point number. Special cases:
    - If the numerator and the denominator are both 0, then this method returns `Double​.NaN`.
    - If only the denominator is zero, then this method returns positive infinity or negative infinity accordingly the numerator sign.
    Specified by:
      `doubleValue` in class `Number`
    Returns:
      this fraction as a floating point number.

  - ### floatValue

    public float floatValue()
    Returns the fraction as a single-precision floating point number. Special cases:
    - If the numerator and the denominator are both 0, then this method returns `Float​.NaN`.
    - If only the denominator is zero, then this method returns positive infinity or negative infinity accordingly the numerator sign.
    Specified by:
      `floatValue` in class `Number`
    Returns:
      this fraction as a floating point number.

  - ### longValue

    public long longValue()
    Returns this fraction rounded toward zero. If the fraction value is NaN, then this method returns 0. If the fraction value is positive or negative infinity, then this method returns `Long​.MAX_VALUE` or `Long​.MIN_VALUE` respectively.
    Specified by:
      `longValue` in class `Number`
    Returns:
      this fraction rounded toward zero.

  - ### intValue

    public int intValue()
    Returns this fraction rounded toward zero. If the fraction value is NaN, then this method returns 0. If the fraction value is positive or negative infinity, then this method returns `Integer​.MAX_VALUE` or `Integer​.MIN_VALUE` respectively.
    Specified by:
      `intValue` in class `Number`
    Returns:
      `numerator` / `denominator` rounded toward zero.
    See Also:
      - `round()`
      - `floor()`
      - `ceil()`

  - ### isNaN

    public boolean isNaN()
    Returns `true` if the numerator and denominator are both zero.
    Returns:
      whether this fraction is 0/0.
    Since:
      1.4

  - ### signum

    public int signum()
    Returns the sign of this fraction. The return value is -1 if this fraction is negative; 0 if the numerator is zero; and 1 if this fraction is positive.
    Returns:
      the sign of this fraction.
    Since:
      1.0
    See Also:
      - `Integer​.signum(int)`

  - ### compareTo

    public int compareTo(Fraction other)
    Compares this fraction with the given one for order.
    Specified by:
      `compareTo` in interface `Comparable<Fraction>`
    Parameters:
      `other` - the fraction to compare to this fraction for ordering.
    Returns:
      a negative number if this fraction is smaller than the given fraction, a positive number if greater, or 0 if equals.

  - ### equals

    public boolean equals(Object other)
    Compares this fraction with the given object for equality. This method returns `true` only if the two objects are fractions with same numerator and denominator values. Fractions with different values are not considered equal even if the two fraction are equivalent.
    Overrides:
      `equals` in class `Object`
    Parameters:
      `other` - the object to compare with this fraction for equality.
    Returns:
      `true` if the given object is another fraction with the same numerator and denominator values.

  - ### hashCode

    public int hashCode()
    Returns a hash code value for this fraction.
    Overrides:
      `hashCode` in class `Object`

  - ### toString

    public String toString()
    Returns a string representation of this fraction. This method returns Unicode symbol if possible.
    Overrides:
      `toString` in class `Object`
    Returns:
      a string representation of this fraction.