Package org.apache.commons.numbers.fraction

Class BigFraction

    • Method Detail

      • from

        public static BigFraction from​(double value)
        Create a fraction given the double value.

        This factory method behaves differently to the method from(double, double, int). It converts the double value exactly, considering its internal bits representation. This works for all values except NaN and infinities and does not requires any loop or convergence threshold.

        Since this conversion is exact and since double numbers are sometimes approximated, the fraction created may seem strange in some cases. For example, calling from(1.0 / 3.0) does not create the fraction \( \frac{1}{3} \), but the fraction \( \frac{6004799503160661}{18014398509481984} \) because the double number passed to the method is not exactly \( \frac{1}{3} \) (which cannot be represented exactly in IEEE754).

        Parameters:
        value - Value to convert to a fraction.
        Returns:
        a new instance.
        Throws:
        IllegalArgumentException - if the given value is NaN or infinite.
        See Also:
        from(double,double,int)

      • from

        public static BigFraction 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:
        IllegalArgumentException - if the given value is NaN or infinite; epsilon is not positive; or maxIterations < 1.
        ArithmeticException - if the continued fraction failed to converge.

      • from

        public static BigFraction 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:
        IllegalArgumentException - if the given value is NaN or infinite or maxDenominator is zero.
        ArithmeticException - if the continued fraction failed to converge.

      • of

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

      • of

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

      • of

        public static BigFraction of​(BigInteger num)
        Create a fraction given the numerator. The denominator is 1.
        Parameters:
        num - Numerator.
        Returns:
        a new instance.
        Throws:
        NullPointerException - if numerator is null.

      • of

        public static BigFraction 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:
        ArithmeticException - if den is zero.

      • of

        public static BigFraction of​(long num,
                             long 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:
        ArithmeticException - if den is zero.

      • of

        public static BigFraction of​(BigInteger num,
                             BigInteger 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:
        NullPointerException - if numerator or denominator are null.
        ArithmeticException - if the denominator is zero.

      • parse

        public static BigFraction parse​(String s)
        Returns a BigFraction 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 BigFraction.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 BigInteger(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 BigFraction are shown below: 

         "0"                 = BigFraction.of(0)
 "42"                = BigFraction.of(42)
 "0 / 1"             = BigFraction.of(0, 1)
 "1 / 3"             = BigFraction.of(1, 3)
 "-4 / 13"           = BigFraction.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 BigFraction.parse(s).toString().equals(s) may not be true.

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

      • zero

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

      • isZero

        public boolean isZero()
        Check if this is a neutral element of addition, i.e. this.add(a) returns a or an element representing the same value as a.

        The default implementation calls equals(zero()). Implementations may want to employ more a efficient method. This may even be required if an implementation has multiple representations of zero and its equals method differentiates between them.

        Specified by:
        isZero in interface Addition<BigFraction>
        Returns:
        true if this is a neutral element of addition.
        See Also:
        Addition.zero()

      • isOne

        public boolean isOne()
        Check if this is a neutral element of multiplication, i.e. this.multiply(a) returns a or an element representing the same value as a.

        The default implementation calls equals(one()). Implementations may want to employ more a efficient method. This may even be required if an implementation has multiple representations of one and its equals method differentiates between them.

        Specified by:
        isOne in interface Multiplication<BigFraction>
        Returns:
        true if this is a neutral element of multiplication.
        See Also:
        Multiplication.one()

      • getNumerator

        public BigInteger getNumerator()
        Access the numerator as a BigInteger.
        Returns:
        the numerator as a BigInteger.

      • getNumeratorAsInt

        public int getNumeratorAsInt()
        Access the numerator as an int.
        Returns:
        the numerator as an int.

      • getNumeratorAsLong

        public long getNumeratorAsLong()
        Access the numerator as a long.
        Returns:
        the numerator as a long.

      • getDenominator

        public BigInteger getDenominator()
        Access the denominator as a BigInteger.
        Returns:
        the denominator as a BigInteger.

      • getDenominatorAsInt

        public int getDenominatorAsInt()
        Access the denominator as an int.
        Returns:
        the denominator as an int.

      • getDenominatorAsLong

        public long getDenominatorAsLong()
        Access the denominator as a long.
        Returns:
        the denominator as a long.

      • 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 BigFraction abs()
        Returns the absolute value of this fraction.
        Returns:
        the absolute value.

      • doubleValue

        public double doubleValue()
        Returns the double value closest to this fraction.
        Specified by:
        doubleValue in class Number
        Returns:
        the fraction as a double.

      • floatValue

        public float floatValue()
        Returns the float value closest to this fraction.
        Specified by:
        floatValue in class Number
        Returns:
        the fraction as a double.

      • intValue

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

      • bigDecimalValue

        public BigDecimal bigDecimalValue()
        Returns the BigDecimal representation of this fraction. This calculates the fraction as numerator divided by denominator.
        Returns:
        the fraction as a BigDecimal.
        Throws:
        ArithmeticException - if the exact quotient does not have a terminating decimal expansion.
        See Also:
        BigDecimal

      • bigDecimalValue

        public BigDecimal bigDecimalValue​(RoundingMode roundingMode)
        Returns the BigDecimal representation of this fraction. This calculates the fraction as numerator divided by denominator following the passed rounding mode.
        Parameters:
        roundingMode - Rounding mode to apply.
        Returns:
        the fraction as a BigDecimal.
        See Also:
        BigDecimal

      • bigDecimalValue

        public BigDecimal bigDecimalValue​(int scale,
                                  RoundingMode roundingMode)
        Returns the BigDecimal representation of this fraction. This calculates the fraction as numerator divided by denominator following the passed scale and rounding mode.
        Parameters:
        scale - scale of the BigDecimal quotient to be returned. see BigDecimal for more information.
        roundingMode - Rounding mode to apply.
        Returns:
        the fraction as a BigDecimal.
        Throws:
        ArithmeticException - if roundingMode == RoundingMode.UNNECESSARY and the specified scale is insufficient to represent the result of the division exactly.
        See Also:
        BigDecimal

      • add

        public BigFraction add​(int value)
        Adds the specified value to this fraction, returning the result in reduced form.
        Parameters:
        value - Value to add.
        Returns:
        this + value.

      • add

        public BigFraction add​(long value)
        Adds the specified value to this fraction, returning the result in reduced form.
        Parameters:
        value - Value to add.
        Returns:
        this + value.

      • add

        public BigFraction add​(BigInteger value)
        Adds the specified value to this fraction, returning the result in reduced form.
        Parameters:
        value - Value to add.
        Returns:
        this + value.

      • add

        public BigFraction add​(BigFraction value)
        Adds the specified value to this fraction, returning the result in reduced form.
        Specified by:
        add in interface Addition<BigFraction>
        Parameters:
        value - Value to add.
        Returns:
        this + value.

      • subtract

        public BigFraction subtract​(int value)
        Subtracts the specified value from this fraction, returning the result in reduced form.
        Parameters:
        value - Value to subtract.
        Returns:
        this - value.

      • subtract

        public BigFraction subtract​(long value)
        Subtracts the specified value from this fraction, returning the result in reduced form.
        Parameters:
        value - Value to subtract.
        Returns:
        this - value.

      • subtract

        public BigFraction subtract​(BigInteger value)
        Subtracts the specified value from this fraction, returning the result in reduced form.
        Parameters:
        value - Value to subtract.
        Returns:
        this - value.

      • multiply

        public BigFraction multiply​(int value)
        Multiply this fraction by the passed value, returning the result in reduced form.
        Specified by:
        multiply in interface NativeOperators<BigFraction>
        Parameters:
        value - Value to multiply by.
        Returns:
        this * value.

      • multiply

        public BigFraction multiply​(long value)
        Multiply this fraction by the passed value, returning the result in reduced form.
        Parameters:
        value - Value to multiply by.
        Returns:
        this * value.

      • multiply

        public BigFraction multiply​(BigInteger value)
        Multiply this fraction by the passed value, returning the result in reduced form.
        Parameters:
        value - Value to multiply by.
        Returns:
        this * value.

      • divide

        public BigFraction 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:
        ArithmeticException - if the value to divide by is zero

      • divide

        public BigFraction divide​(long value)
        Divide this fraction by the passed value, returning the result in reduced form.
        Parameters:
        value - Value to divide by
        Returns:
        this / value.
        Throws:
        ArithmeticException - if the value to divide by is zero

      • divide

        public BigFraction divide​(BigInteger value)
        Divide this fraction by the passed value, returning the result in reduced form.
        Parameters:
        value - Value to divide by
        Returns:
        this / value.
        Throws:
        ArithmeticException - if the value to divide by is zero

      • pow

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

      • toString

        public 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 Object
        Returns:
        a string representation of the fraction.

      • equals

        public boolean equals​(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 Object
        Parameters:
        other -
        Returns: