Class Fraction

    • Field Summary

      Fields 
      Modifier and Type Field Description
      private static double DEFAULT_EPSILON
      The default epsilon used for convergence.
      private static int DEFAULT_MAX_ITERATIONS
      The default iterations used for convergence.
      private int denominator
      The denominator of this fraction reduced to lowest terms.
      private static java.lang.String NOT_FINITE
      Message for non-finite input double argument to factory constructors.
      private int numerator
      The numerator of this fraction reduced to lowest terms.
      static Fraction ONE
      A fraction representing "1".
      private static long OVERFLOW
      The overflow limit for conversion from a double (2^31).
      private static long serialVersionUID
      Serializable version identifier.
      static Fraction ZERO
      A fraction representing "0".
    • Constructor Summary

      Constructors 
      Modifier Constructor Description
      private Fraction​(double value, double epsilon, int maxDenominator, int maxIterations)
      Create a fraction given the double value and either the maximum error allowed or the maximum number of denominator digits.
      private Fraction​(int num)
      Private constructor: Instances are created using factory methods.
      private Fraction​(int num, int den)
      Private constructor: Instances are created using factory methods.
    • Method Summary

      All Methods Static Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      Fraction abs()
      Returns the absolute value of this fraction.
      Fraction add​(int value)
      Adds the specified value to this fraction, returning the result in reduced form.
      Fraction add​(Fraction value)
      Adds the specified value to this fraction, returning the result in reduced form.
      private Fraction addSub​(Fraction value, boolean isAdd)
      Implements add and subtract using algorithm described in Knuth 4.5.1.
      int compareTo​(Fraction other)
      Compares this object with the specified object for order using the signed magnitude.
      Fraction divide​(int value)
      Divide this fraction by the passed value, returning the result in reduced form.
      Fraction divide​(Fraction value)
      Divide this fraction by the passed value, returning the result in reduced form.
      double doubleValue()
      Returns the double value closest to this fraction.
      boolean equals​(java.lang.Object other)
      Test for equality with another object.
      float floatValue()
      Returns the float value closest to this fraction.
      static Fraction from​(double value)
      Create a fraction given the double value.
      static Fraction from​(double value, double epsilon, int maxIterations)
      Create a fraction given the double value and maximum error allowed.
      static Fraction from​(double value, int maxDenominator)
      Create a fraction given the double value and maximum denominator.
      int getDenominator()
      Access the denominator as an int.
      int getNumerator()
      Access the numerator as an int.
      int hashCode()  
      int intValue()
      Returns the whole number part of the fraction.
      private boolean isZero()
      Returns true if this fraction is zero.
      long longValue()
      Returns the whole number part of the fraction.
      Fraction multiply​(int value)
      Multiply this fraction by the passed value, returning the result in reduced form.
      private Fraction multiply​(int num, int den)
      Multiply this fraction by the passed fraction decomposed into a numerator and denominator, returning the result in reduced form.
      Fraction multiply​(Fraction value)
      Multiply this fraction by the passed value, returning the result in reduced form.
      Fraction negate()
      Additive inverse.
      static Fraction of​(int num)
      Create a fraction given the numerator.
      static Fraction of​(int num, int den)
      Create a fraction given the numerator and denominator.
      Fraction one()
      Identity element.
      static Fraction parse​(java.lang.String s)
      Returns a Fraction instance representing the specified string s.
      Fraction pow​(int exponent)
      Returns a Fraction whose value is thisexponent, returning the result in reduced form.
      Fraction reciprocal()
      Multiplicative inverse.
      int signum()
      Retrieves the sign of this fraction.
      Fraction subtract​(int value)
      Subtracts the specified value from this fraction, returning the result in reduced form.
      Fraction subtract​(Fraction value)
      Subtracts the specified value from this fraction, returning the result in reduced form.
      java.lang.String toString()
      Returns the String representing this fraction.
      Fraction zero()
      Identity element.
      • Methods inherited from class java.lang.Number

        byteValue, shortValue
      • Methods inherited from class java.lang.Object

        clone, finalize, getClass, notify, notifyAll, wait, wait, wait
    • Field Detail

      • ZERO

        public static final Fraction ZERO
        A fraction representing "0".
      • ONE

        public static final Fraction ONE
        A fraction representing "1".
      • serialVersionUID

        private static final long serialVersionUID
        Serializable version identifier.
        See Also:
        Constant Field Values
      • DEFAULT_EPSILON

        private static final double DEFAULT_EPSILON
        The default epsilon used for convergence.
        See Also:
        Constant Field Values
      • DEFAULT_MAX_ITERATIONS

        private static final int DEFAULT_MAX_ITERATIONS
        The default iterations used for convergence.
        See Also:
        Constant Field Values
      • NOT_FINITE

        private static final java.lang.String NOT_FINITE
        Message for non-finite input double argument to factory constructors.
        See Also:
        Constant Field Values
      • OVERFLOW

        private static final long OVERFLOW
        The overflow limit for conversion from a double (2^31).
        See Also:
        Constant Field Values
      • numerator

        private final int numerator
        The numerator of this fraction reduced to lowest terms.
      • denominator

        private final int denominator
        The denominator of this fraction reduced to lowest terms.
    • Constructor Detail

      • Fraction

        private Fraction​(int num,
                         int den)
        Private constructor: Instances are created using factory methods.

        This constructor should only be invoked when the fraction is known to be non-zero; otherwise use ZERO. This avoids creating the zero representation 0 / -1.

        Parameters:
        num - Numerator.
        den - Denominator.
        Throws:
        java.lang.ArithmeticException - if the denominator is zero.
      • Fraction

        private Fraction​(int num)
        Private constructor: Instances are created using factory methods.

        This sets the denominator to 1.

        Parameters:
        num - Numerator.
      • Fraction

        private Fraction​(double value,
                         double epsilon,
                         int maxDenominator,
                         int maxIterations)
        Create a fraction given the double value and either the maximum error allowed or the maximum number of denominator digits.

        NOTE: This constructor is called with:

        • EITHER a valid epsilon value and the maxDenominator set to Integer.MAX_VALUE (that way the maxDenominator has no effect)
        • OR a valid maxDenominator value and the epsilon value set to zero (that way epsilon only has effect if there is an exact match before the maxDenominator value is reached).

        It has been done this way so that the same code can be reused for both scenarios. However this could be confusing to users if it were part of the public API and this method should therefore remain PRIVATE.

        See JIRA issue ticket MATH-181 for more details: https://issues.apache.org/jira/browse/MATH-181

        Warning: This conversion assumes the value is not zero.

        Parameters:
        value - Value to convert to a fraction. Must not be zero.
        epsilon - Maximum error allowed. The resulting fraction is within epsilon of value, in absolute terms.
        maxDenominator - Maximum denominator value allowed.
        maxIterations - Maximum number of convergents.
        Throws:
        java.lang.IllegalArgumentException - if the given value is NaN or infinite.
        java.lang.ArithmeticException - if the continued fraction failed to converge.
    • Method Detail

      • from

        public static Fraction from​(double value)
        Create a fraction given the double value.
        Parameters:
        value - Value to convert to a fraction.
        Returns:
        a new instance.
        Throws:
        java.lang.IllegalArgumentException - if the given value is NaN or infinite.
        java.lang.ArithmeticException - if the continued fraction failed to converge.
      • from

        public static Fraction from​(double value,
                                    double epsilon,
                                    int maxIterations)
        Create a fraction given the double value and maximum error allowed.

        References:

        Parameters:
        value - Value to convert to a fraction.
        epsilon - Maximum error allowed. The resulting fraction is within epsilon of value, in absolute terms.
        maxIterations - Maximum number of convergents.
        Returns:
        a new instance.
        Throws:
        java.lang.IllegalArgumentException - if the given value is NaN or infinite; epsilon is not positive; or maxIterations < 1.
        java.lang.ArithmeticException - if the continued fraction failed to converge.
      • from

        public static Fraction from​(double value,
                                    int maxDenominator)
        Create a fraction given the double value and maximum denominator.

        References:

        Note: The magnitude of the maxDenominator is used allowing use of Integer.MIN_VALUE for a supported maximum denominator of 231.

        Parameters:
        value - Value to convert to a fraction.
        maxDenominator - Maximum allowed value for denominator.
        Returns:
        a new instance.
        Throws:
        java.lang.IllegalArgumentException - if the given value is NaN or infinite or maxDenominator is zero.
        java.lang.ArithmeticException - if the continued fraction failed to converge.
      • of

        public static Fraction of​(int num)
        Create a fraction given the numerator. The denominator is 1.
        Parameters:
        num - Numerator.
        Returns:
        a new instance.
      • of

        public static Fraction of​(int num,
                                  int den)
        Create a fraction given the numerator and denominator. The fraction is reduced to lowest terms.
        Parameters:
        num - Numerator.
        den - Denominator.
        Returns:
        a new instance.
        Throws:
        java.lang.ArithmeticException - if the denominator is zero.
      • parse

        public static Fraction parse​(java.lang.String s)
        Returns a Fraction instance representing the specified string s.

        If s is null, then a NullPointerException is thrown.

        The string must be in a format compatible with that produced by Fraction.toString(). The format expects an integer optionally followed by a '/' character and and second integer. Leading and trailing spaces are allowed around each numeric part. Each numeric part is parsed using Integer.parseInt(String). The parts are interpreted as the numerator and optional denominator of the fraction. If absent the denominator is assumed to be "1".

        Examples of valid strings and the equivalent Fraction are shown below:

         "0"                 = Fraction.of(0)
         "42"                = Fraction.of(42)
         "0 / 1"             = Fraction.of(0, 1)
         "1 / 3"             = Fraction.of(1, 3)
         "-4 / 13"           = Fraction.of(-4, 13)

        Note: The fraction is returned in reduced form and the numerator and denominator may not match the values in the input string. For this reason the result of Fraction.parse(s).toString().equals(s) may not be true.

        Parameters:
        s - String representation.
        Returns:
        an instance.
        Throws:
        java.lang.NullPointerException - if the string is null.
        java.lang.NumberFormatException - if the string does not contain a parsable fraction.
        See Also:
        Integer.parseInt(String), toString()
      • zero

        public Fraction zero()
        Description copied from interface: Addition
        Identity element.
        Specified by:
        zero in interface Addition<Fraction>
        Returns:
        the field element such that for all a, zero().add(a).equals(a) is true.
      • one

        public Fraction one()
        Description copied from interface: Multiplication
        Identity element.
        Specified by:
        one in interface Multiplication<Fraction>
        Returns:
        the field element such that for all a, one().multiply(a).equals(a) is true.
      • getNumerator

        public int getNumerator()
        Access the numerator as an int.
        Returns:
        the numerator as an int.
      • getDenominator

        public int getDenominator()
        Access the denominator as an int.
        Returns:
        the denominator as an int.
      • signum

        public int signum()
        Retrieves the sign of this fraction.
        Returns:
        -1 if the value is strictly negative, 1 if it is strictly positive, 0 if it is 0.
      • abs

        public Fraction abs()
        Returns the absolute value of this fraction.
        Returns:
        the absolute value.
      • reciprocal

        public Fraction reciprocal()
        Multiplicative inverse.

        Raises an exception if the fraction is equal to zero.

        Specified by:
        reciprocal in interface Multiplication<Fraction>
        Returns:
        this-1.
        Throws:
        java.lang.ArithmeticException - if the current numerator is zero
      • doubleValue

        public double doubleValue()
        Returns the double value closest to this fraction. This calculates the fraction as numerator divided by denominator.
        Specified by:
        doubleValue in class java.lang.Number
        Returns:
        the fraction as a double.
      • floatValue

        public float floatValue()
        Returns the float value closest to this fraction. This calculates the fraction as numerator divided by denominator.
        Specified by:
        floatValue in class java.lang.Number
        Returns:
        the fraction as a float.
      • intValue

        public int intValue()
        Returns the whole number part of the fraction.
        Specified by:
        intValue in class java.lang.Number
        Returns:
        the largest int value that is not larger than this fraction.
      • longValue

        public long longValue()
        Returns the whole number part of the fraction.
        Specified by:
        longValue in class java.lang.Number
        Returns:
        the largest long value that is not larger than this fraction.
      • add

        public Fraction add​(int value)
        Adds the specified value to this fraction, returning the result in reduced form.
        Parameters:
        value - Value to add.
        Returns:
        this + value.
        Throws:
        java.lang.ArithmeticException - if the resulting numerator cannot be represented in an int.
      • add

        public Fraction add​(Fraction value)
        Adds the specified value to this fraction, returning the result in reduced form.
        Specified by:
        add in interface Addition<Fraction>
        Parameters:
        value - Value to add.
        Returns:
        this + value.
        Throws:
        java.lang.ArithmeticException - if the resulting numerator or denominator cannot be represented in an int.
      • subtract

        public Fraction subtract​(int value)
        Subtracts the specified value from this fraction, returning the result in reduced form.
        Parameters:
        value - Value to subtract.
        Returns:
        this - value.
        Throws:
        java.lang.ArithmeticException - if the resulting numerator cannot be represented in an int.
      • subtract

        public Fraction subtract​(Fraction value)
        Subtracts the specified value from this fraction, returning the result in reduced form.
        Specified by:
        subtract in interface NativeOperators<Fraction>
        Parameters:
        value - Value to subtract.
        Returns:
        this - value.
        Throws:
        java.lang.ArithmeticException - if the resulting numerator or denominator cannot be represented in an int.
      • addSub

        private Fraction addSub​(Fraction value,
                                boolean isAdd)
        Implements add and subtract using algorithm described in Knuth 4.5.1.
        Parameters:
        value - Fraction to add or subtract.
        isAdd - Whether the operation is "add" or "subtract".
        Returns:
        a new instance.
        Throws:
        java.lang.ArithmeticException - if the resulting numerator or denominator cannot be represented in an int.
      • multiply

        public Fraction multiply​(int value)
        Multiply this fraction by the passed value, returning the result in reduced form.
        Specified by:
        multiply in interface NativeOperators<Fraction>
        Parameters:
        value - Value to multiply by.
        Returns:
        this * value.
        Throws:
        java.lang.ArithmeticException - if the resulting numerator cannot be represented in an int.
      • multiply

        public Fraction multiply​(Fraction value)
        Multiply this fraction by the passed value, returning the result in reduced form.
        Specified by:
        multiply in interface Multiplication<Fraction>
        Parameters:
        value - Value to multiply by.
        Returns:
        this * value.
        Throws:
        java.lang.ArithmeticException - if the resulting numerator or denominator cannot be represented in an int.
      • multiply

        private Fraction multiply​(int num,
                                  int den)
        Multiply this fraction by the passed fraction decomposed into a numerator and denominator, returning the result in reduced form.

        This is a utility method to be used by multiply and divide. The decomposed fraction arguments and this fraction are not checked for zero.

        Parameters:
        num - Fraction numerator.
        den - Fraction denominator.
        Returns:
        this * num / den.
        Throws:
        java.lang.ArithmeticException - if the resulting numerator or denominator cannot be represented in an int.
      • divide

        public Fraction divide​(int value)
        Divide this fraction by the passed value, returning the result in reduced form.
        Parameters:
        value - Value to divide by
        Returns:
        this / value.
        Throws:
        java.lang.ArithmeticException - if the value to divide by is zero or if the resulting numerator or denominator cannot be represented by an int.
      • divide

        public Fraction divide​(Fraction value)
        Divide this fraction by the passed value, returning the result in reduced form.
        Specified by:
        divide in interface NativeOperators<Fraction>
        Parameters:
        value - Value to divide by
        Returns:
        this / value.
        Throws:
        java.lang.ArithmeticException - if the value to divide by is zero or if the resulting numerator or denominator cannot be represented by an int.
      • pow

        public Fraction pow​(int exponent)
        Returns a Fraction whose value is thisexponent, returning the result in reduced form.
        Specified by:
        pow in interface NativeOperators<Fraction>
        Parameters:
        exponent - exponent to which this Fraction is to be raised.
        Returns:
        thisexponent.
        Throws:
        java.lang.ArithmeticException - if the intermediate result would overflow.
      • toString

        public java.lang.String toString()
        Returns the String representing this fraction. Uses:
        • "0" if numerator is zero.
        • "numerator" if denominator is one.
        • "numerator / denominator" for all other cases.
        Overrides:
        toString in class java.lang.Object
        Returns:
        a string representation of the fraction.
      • compareTo

        public int compareTo​(Fraction other)
        Compares this object with the specified object for order using the signed magnitude.
        Specified by:
        compareTo in interface java.lang.Comparable<Fraction>
        Parameters:
        other -
        Returns:
      • equals

        public boolean equals​(java.lang.Object other)
        Test for equality with another object. If the other object is a Fraction then a comparison is made of the sign and magnitude; otherwise false is returned.
        Overrides:
        equals in class java.lang.Object
        Parameters:
        other -
        Returns:
      • hashCode

        public int hashCode()
        Overrides:
        hashCode in class java.lang.Object
      • isZero

        private boolean isZero()
        Returns true if this fraction is zero.
        Returns:
        true if zero