Package org.apache.commons.lang3.math

Class Fraction

java.lang.Object
java.lang.Number
org.apache.commons.lang3.math.Fraction
All Implemented Interfaces:
Serializable, Comparable<Fraction>
public final class Fraction extends Number implements Comparable<Fraction>
Fraction is a Number implementation that stores fractions accurately.

This class is immutable, and interoperable with most methods that accept a Number.

Note that this class is intended for common use cases, it is int based and thus suffers from various overflow issues. For a BigInteger based equivalent, please see the Commons Math BigFraction class.

Since:
2.0
See Also:

  • Field Details

    • serialVersionUID

      private static final long serialVersionUID
      Required for serialization support. Lang version 2.0.
      See Also:

    • ZERO

      public static final Fraction ZERO
      Fraction representation of 0.

    • ONE

      public static final Fraction ONE
      Fraction representation of 1.

    • ONE_HALF

      public static final Fraction ONE_HALF
      Fraction representation of 1/2.

    • ONE_THIRD

      public static final Fraction ONE_THIRD
      Fraction representation of 1/3.

    • TWO_THIRDS

      public static final Fraction TWO_THIRDS
      Fraction representation of 2/3.

    • ONE_QUARTER

      public static final Fraction ONE_QUARTER
      Fraction representation of 1/4.

    • TWO_QUARTERS

      public static final Fraction TWO_QUARTERS
      Fraction representation of 2/4.

    • THREE_QUARTERS

      public static final Fraction THREE_QUARTERS
      Fraction representation of 3/4.

    • ONE_FIFTH

      public static final Fraction ONE_FIFTH
      Fraction representation of 1/5.

    • TWO_FIFTHS

      public static final Fraction TWO_FIFTHS
      Fraction representation of 2/5.

    • THREE_FIFTHS

      public static final Fraction THREE_FIFTHS
      Fraction representation of 3/5.

    • FOUR_FIFTHS

      public static final Fraction FOUR_FIFTHS
      Fraction representation of 4/5.

    • numerator

      private final int numerator
      The numerator number part of the fraction (the three in three sevenths).

    • denominator

      private final int denominator
      The denominator number part of the fraction (the seven in three sevenths).

    • hashCode

      private transient int hashCode
      Cached output hashCode (class is immutable).

    • toString

      private transient String toString
      Cached output toString (class is immutable).

    • toProperString

      private transient String toProperString
      Cached output toProperString (class is immutable).

  • Constructor Details

    • Fraction

      private Fraction(int numerator, int denominator)
      Constructs a Fraction instance with the 2 parts of a fraction Y/Z.
      Parameters:
      numerator - the numerator, for example the three in 'three sevenths'
      denominator - the denominator, for example the seven in 'three sevenths'

  • Method Details

    • addAndCheck

      private static int addAndCheck(int x, int y)
      Add two integers, checking for overflow.
      Parameters:
      x - an addend
      y - an addend
      Returns:
      the sum x+y
      Throws:
      ArithmeticException - if the result can not be represented as an int

    • getFraction

      public static Fraction getFraction(double value)
      Creates a Fraction instance from a double value.

      This method uses the continued fraction algorithm, computing a maximum of 25 convergents and bounding the denominator by 10,000.

      Parameters:
      value - the double value to convert
      Returns:
      a new fraction instance that is close to the value
      Throws:
      ArithmeticException - if |value| &gt; Integer.MAX_VALUE or value = NaN
      ArithmeticException - if the calculated denominator is zero
      ArithmeticException - if the algorithm does not converge

    • getFraction

      public static Fraction getFraction(int numerator, int denominator)
      Creates a Fraction instance with the 2 parts of a fraction Y/Z.

      Any negative signs are resolved to be on the numerator.

      Parameters:
      numerator - the numerator, for example the three in 'three sevenths'
      denominator - the denominator, for example the seven in 'three sevenths'
      Returns:
      a new fraction instance
      Throws:
      ArithmeticException - if the denominator is zero or the denominator is negative and the numerator is Integer#MIN_VALUE

    • getFraction

      public static Fraction getFraction(int whole, int numerator, int denominator)
      Creates a Fraction instance with the 3 parts of a fraction X Y/Z.

      The negative sign must be passed in on the whole number part.

      Parameters:
      whole - the whole number, for example the one in 'one and three sevenths'
      numerator - the numerator, for example the three in 'one and three sevenths'
      denominator - the denominator, for example the seven in 'one and three sevenths'
      Returns:
      a new fraction instance
      Throws:
      ArithmeticException - if the denominator is zero
      ArithmeticException - if the denominator is negative
      ArithmeticException - if the numerator is negative
      ArithmeticException - if the resulting numerator exceeds Integer.MAX_VALUE

    • getFraction

      public static Fraction getFraction(String str)
      Creates a Fraction from a String.

      The formats accepted are:

      1. double String containing a dot
      2. 'X Y/Z'
      3. 'Y/Z'
      4. 'X' (a simple whole number)

      and a .

      Parameters:
      str - the string to parse, must not be null
      Returns:
      the new Fraction instance
      Throws:
      NullPointerException - if the string is null
      NumberFormatException - if the number format is invalid

    • getReducedFraction

      public static Fraction getReducedFraction(int numerator, int denominator)
      Creates a reduced Fraction instance with the 2 parts of a fraction Y/Z.

      For example, if the input parameters represent 2/4, then the created fraction will be 1/2.

      Any negative signs are resolved to be on the numerator.

      Parameters:
      numerator - the numerator, for example the three in 'three sevenths'
      denominator - the denominator, for example the seven in 'three sevenths'
      Returns:
      a new fraction instance, with the numerator and denominator reduced
      Throws:
      ArithmeticException - if the denominator is zero

    • greatestCommonDivisor

      private static int greatestCommonDivisor(int u, int v)
      Gets the greatest common divisor of the absolute value of two numbers, using the "binary gcd" method which avoids division and modulo operations. See Knuth 4.5.2 algorithm B. This algorithm is due to Josef Stein (1961).
      Parameters:
      u - a non-zero number
      v - a non-zero number
      Returns:
      the greatest common divisor, never zero

    • mulAndCheck

      private static int mulAndCheck(int x, int y)
      Multiply two integers, checking for overflow.
      Parameters:
      x - a factor
      y - a factor
      Returns:
      the product x*y
      Throws:
      ArithmeticException - if the result can not be represented as an int

    • mulPosAndCheck

      private static int mulPosAndCheck(int x, int y)
      Multiply two non-negative integers, checking for overflow.
      Parameters:
      x - a non-negative factor
      y - a non-negative factor
      Returns:
      the product x*y
      Throws:
      ArithmeticException - if the result can not be represented as an int

    • subAndCheck

      private static int subAndCheck(int x, int y)
      Subtract two integers, checking for overflow.
      Parameters:
      x - the minuend
      y - the subtrahend
      Returns:
      the difference x-y
      Throws:
      ArithmeticException - if the result can not be represented as an int

    • abs

      public Fraction abs()
      Gets a fraction that is the positive equivalent of this one.

      More precisely: (fraction &gt;= 0 ? this : -fraction)

      The returned fraction is not reduced.

      Returns:
      this if it is positive, or a new positive fraction instance with the opposite signed numerator

    • add

      public Fraction add(Fraction fraction)
      Adds the value of this fraction to another, returning the result in reduced form. The algorithm follows Knuth, 4.5.1.
      Parameters:
      fraction - the fraction to add, must not be null
      Returns:
      a Fraction instance with the resulting values
      Throws:
      NullPointerException - if the fraction is null
      ArithmeticException - if the resulting numerator or denominator exceeds Integer.MAX_VALUE

    • addSub

      private Fraction addSub(Fraction fraction, boolean isAdd)
      Implement add and subtract using algorithm described in Knuth 4.5.1.
      Parameters:
      fraction - the fraction to subtract, must not be null
      isAdd - true to add, false to subtract
      Returns:
      a Fraction instance with the resulting values
      Throws:
      IllegalArgumentException - if the fraction is null
      ArithmeticException - if the resulting numerator or denominator cannot be represented in an int.

    • compareTo

      public int compareTo(Fraction other)
      Compares this object to another based on size.

      Note: this class has a natural ordering that is inconsistent with equals, because, for example, equals treats 1/2 and 2/4 as different, whereas compareTo treats them as equal.

      Specified by:
      compareTo in interface Comparable<Fraction>
      Parameters:
      other - the object to compare to
      Returns:
      -1 if this is less, 0 if equal, +1 if greater
      Throws:
      ClassCastException - if the object is not a Fraction
      NullPointerException - if the object is null

    • divideBy

      public Fraction divideBy(Fraction fraction)
      Divide the value of this fraction by another.
      Parameters:
      fraction - the fraction to divide by, must not be null
      Returns:
      a Fraction instance with the resulting values
      Throws:
      NullPointerException - if the fraction is null
      ArithmeticException - if the fraction to divide by is zero
      ArithmeticException - if the resulting numerator or denominator exceeds Integer.MAX_VALUE

    • doubleValue

      public double doubleValue()
      Gets the fraction as a double. This calculates the fraction as the numerator divided by denominator.
      Specified by:
      doubleValue in class Number
      Returns:
      the fraction as a double

    • equals

      public boolean equals(Object obj)
      Compares this fraction to another object to test if they are equal..

      To be equal, both values must be equal. Thus 2/4 is not equal to 1/2.

      Overrides:
      equals in class Object
      Parameters:
      obj - the reference object with which to compare
      Returns:
      true if this object is equal

    • floatValue

      public float floatValue()
      Gets the fraction as a float. This calculates the fraction as the numerator divided by denominator.
      Specified by:
      floatValue in class Number
      Returns:
      the fraction as a float

    • getDenominator

      public int getDenominator()
      Gets the denominator part of the fraction.
      Returns:
      the denominator fraction part

    • getNumerator

      public int getNumerator()
      Gets the numerator part of the fraction.

      This method may return a value greater than the denominator, an improper fraction, such as the seven in 7/4.

      Returns:
      the numerator fraction part

    • getProperNumerator

      public int getProperNumerator()
      Gets the proper numerator, always positive.

      An improper fraction 7/4 can be resolved into a proper one, 1 3/4. This method returns the 3 from the proper fraction.

      If the fraction is negative such as -7/4, it can be resolved into -1 3/4, so this method returns the positive proper numerator, 3.

      Returns:
      the numerator fraction part of a proper fraction, always positive

    • getProperWhole

      public int getProperWhole()
      Gets the proper whole part of the fraction.

      An improper fraction 7/4 can be resolved into a proper one, 1 3/4. This method returns the 1 from the proper fraction.

      If the fraction is negative such as -7/4, it can be resolved into -1 3/4, so this method returns the positive whole part -1.

      Returns:
      the whole fraction part of a proper fraction, that includes the sign

    • hashCode

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

    • intValue

      public int intValue()
      Gets the fraction as an int. This returns the whole number part of the fraction.
      Specified by:
      intValue in class Number
      Returns:
      the whole number fraction part

    • invert

      public Fraction invert()
      Gets a fraction that is the inverse (1/fraction) of this one.

      The returned fraction is not reduced.

      Returns:
      a new fraction instance with the numerator and denominator inverted.
      Throws:
      ArithmeticException - if the fraction represents zero.

    • longValue

      public long longValue()
      Gets the fraction as a long. This returns the whole number part of the fraction.
      Specified by:
      longValue in class Number
      Returns:
      the whole number fraction part

    • multiplyBy

      public Fraction multiplyBy(Fraction fraction)
      Multiplies the value of this fraction by another, returning the result in reduced form.
      Parameters:
      fraction - the fraction to multiply by, must not be null
      Returns:
      a Fraction instance with the resulting values
      Throws:
      NullPointerException - if the fraction is null
      ArithmeticException - if the resulting numerator or denominator exceeds Integer.MAX_VALUE

    • negate

      public Fraction negate()
      Gets a fraction that is the negative (-fraction) of this one.

      The returned fraction is not reduced.

      Returns:
      a new fraction instance with the opposite signed numerator

    • pow

      public Fraction pow(int power)
      Gets a fraction that is raised to the passed in power.

      The returned fraction is in reduced form.

      Parameters:
      power - the power to raise the fraction to
      Returns:
      this if the power is one, ONE if the power is zero (even if the fraction equals ZERO) or a new fraction instance raised to the appropriate power
      Throws:
      ArithmeticException - if the resulting numerator or denominator exceeds Integer.MAX_VALUE

    • reduce

      public Fraction reduce()
      Reduce the fraction to the smallest values for the numerator and denominator, returning the result.

      For example, if this fraction represents 2/4, then the result will be 1/2.

      Returns:
      a new reduced fraction instance, or this if no simplification possible

    • subtract

      public Fraction subtract(Fraction fraction)
      Subtracts the value of another fraction from the value of this one, returning the result in reduced form.
      Parameters:
      fraction - the fraction to subtract, must not be null
      Returns:
      a Fraction instance with the resulting values
      Throws:
      NullPointerException - if the fraction is null
      ArithmeticException - if the resulting numerator or denominator cannot be represented in an int.

    • toProperString

      public String toProperString()
      Gets the fraction as a proper String in the format X Y/Z.

      The format used in 'wholeNumber numerator/denominator'. If the whole number is zero it will be omitted. If the numerator is zero, only the whole number is returned.

      Returns:
      a String form of the fraction

    • toString

      public String toString()
      Gets the fraction as a String.

      The format used is 'numerator/denominator' always.

      Overrides:
      toString in class Object
      Returns:
      a String form of the fraction