Package org.hipparchus.fraction

Class BigFraction

java.lang.Object
java.lang.Number
org.hipparchus.fraction.BigFraction
All Implemented Interfaces:
Serializable, Comparable<BigFraction>, FieldElement<BigFraction>
public class BigFraction extends Number implements FieldElement<BigFraction>, Comparable<BigFraction>, Serializable
Representation of a rational number without any overflow. This class is immutable.
See Also:

  • Field Details

    • TWO

      public static final BigFraction TWO
      A fraction representing "2 / 1".

    • ONE

      public static final BigFraction ONE
      A fraction representing "1".

    • ZERO

      public static final BigFraction ZERO
      A fraction representing "0".

    • MINUS_ONE

      public static final BigFraction MINUS_ONE
      A fraction representing "-1 / 1".

    • FOUR_FIFTHS

      public static final BigFraction FOUR_FIFTHS
      A fraction representing "4/5".

    • ONE_FIFTH

      public static final BigFraction ONE_FIFTH
      A fraction representing "1/5".

    • ONE_HALF

      public static final BigFraction ONE_HALF
      A fraction representing "1/2".

    • ONE_QUARTER

      public static final BigFraction ONE_QUARTER
      A fraction representing "1/4".

    • ONE_THIRD

      public static final BigFraction ONE_THIRD
      A fraction representing "1/3".

    • THREE_FIFTHS

      public static final BigFraction THREE_FIFTHS
      A fraction representing "3/5".

    • THREE_QUARTERS

      public static final BigFraction THREE_QUARTERS
      A fraction representing "3/4".

    • TWO_FIFTHS

      public static final BigFraction TWO_FIFTHS
      A fraction representing "2/5".

    • TWO_QUARTERS

      public static final BigFraction TWO_QUARTERS
      A fraction representing "2/4".

    • TWO_THIRDS

      public static final BigFraction TWO_THIRDS
      A fraction representing "2/3".

  • Constructor Details

    • BigFraction

      public BigFraction(BigInteger num)

      Create a BigFraction equivalent to the passed BigInteger, ie "num / 1".

      Parameters:
      num - the numerator.

    • BigFraction

      public BigFraction(BigInteger num, BigInteger den)
      Create a BigFraction given the numerator and denominator as BigInteger. The BigFraction is reduced to lowest terms.
      Parameters:
      num - the numerator, must not be null.
      den - the denominator, must not be null.
      Throws:
      MathIllegalArgumentException - if the denominator is zero.
      NullArgumentException - if either of the arguments is null

    • BigFraction

      public BigFraction(double value) throws MathIllegalArgumentException
      Create a fraction given the double value.

      This constructor behaves differently from BigFraction(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 new BigFraction(1.0 / 3.0) does not create the fraction 1/3, but the fraction 6004799503160661 / 18014398509481984 because the double number passed to the constructor is not exactly 1/3 (this number cannot be stored exactly in IEEE754).

      Parameters:
      value - the double value to convert to a fraction.
      Throws:
      MathIllegalArgumentException - if value is NaN or infinite
      See Also:

    • BigFraction

      public BigFraction(double value, double epsilon, int maxIterations) throws MathIllegalStateException
      Create a fraction given the double value and maximum error allowed.

      * References:

      Parameters:
      value - the double 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.
      Throws:
      MathIllegalStateException - if the continued fraction failed to converge.
      See Also:

    • BigFraction

      public BigFraction(double value, long maxDenominator) throws MathIllegalStateException
      Create a fraction given the double value and maximum denominator.

      * References:

      Parameters:
      value - the double value to convert to a fraction.
      maxDenominator - The maximum allowed value for denominator.
      Throws:
      MathIllegalStateException - if the continued fraction failed to converge.

    • BigFraction

      public BigFraction(int num)

      Create a BigFraction equivalent to the passed int, ie "num / 1".

      Parameters:
      num - the numerator.

    • BigFraction

      public BigFraction(int num, int den)

      Create a BigFraction given the numerator and denominator as simple int. The BigFraction is reduced to lowest terms.

      Parameters:
      num - the numerator.
      den - the denominator.

    • BigFraction

      public BigFraction(long num)

      Create a BigFraction equivalent to the passed long, ie "num / 1".

      Parameters:
      num - the numerator.

    • BigFraction

      public BigFraction(long num, long den)

      Create a BigFraction given the numerator and denominator as simple long. The BigFraction is reduced to lowest terms.

      Parameters:
      num - the numerator.
      den - the denominator.

  • Method Details

    • convergents

      public static Stream<BigFraction> convergents(double value, int maxConvergents)
      Generate a stream of convergents from a real number.
      Parameters:
      value - value to approximate
      maxConvergents - maximum number of convergents.
      Returns:
      stream of BigFraction convergents approximating value
      Since:
      2.1

    • convergent

      public static Pair<BigFraction,Boolean> convergent(double value, int maxConvergents, BigFraction.ConvergenceTest convergenceTest)
      Returns the last element of the series of convergent-steps to approximate the given value.

      The series terminates either at the first step that satisfies the given convergenceTest or after at most maxConvergents elements. The returned Pair consists of that terminal BigFraction and a Boolean that indicates if it satisfies the given convergence tests. If the returned pair's value is false the element at position maxConvergents was examined but failed to satisfy the convergenceTest. A caller can then decide to accept the result nevertheless or to discard it. This method is usually faster than convergents(double, int) if only the terminal element is of interest.

      Parameters:
      value - value to approximate
      maxConvergents - maximum number of convergents to examine
      convergenceTest - the test if the series has converged at a step
      Returns:
      the pair of last element of the series of convergents and a boolean indicating if that element satisfies the specified convergent test

    • getReal

      public double getReal()
      Get the real value of the number.
      Specified by:
      getReal in interface FieldElement<BigFraction>
      Returns:
      real value

    • getReducedFraction

      public static BigFraction getReducedFraction(int numerator, int denominator)

      Creates a BigFraction 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, with the numerator and denominator reduced.
      Throws:
      ArithmeticException - if the denominator is zero.

    • abs

      public BigFraction abs()

      Returns the absolute value of this BigFraction.

      Returns:
      the absolute value as a BigFraction.

    • isInteger

      public boolean isInteger()
      Check if a fraction is an integer.
      Returns:
      true of fraction is an integer

    • signum

      public int signum()
      Returns the signum function of this BigFraction.

      The return value is -1 if the specified value is negative; 0 if the specified value is zero; and 1 if the specified value is positive.

      Returns:
      the signum function of this BigFraction
      Since:
      1.7

    • add

      public BigFraction add(BigInteger bg) throws NullArgumentException

      Adds the value of this fraction to the passed BigInteger, returning the result in reduced form.

      Parameters:
      bg - the BigInteger to add, must'nt be null.
      Returns:
      a BigFraction instance with the resulting values.
      Throws:
      NullArgumentException - if the BigInteger is null.

    • add

      public BigFraction add(int i)

      Adds the value of this fraction to the passed integer, returning the result in reduced form.

      Parameters:
      i - the integer to add.
      Returns:
      a BigFraction instance with the resulting values.

    • add

      public BigFraction add(long l)

      Adds the value of this fraction to the passed long, returning the result in reduced form.

      Parameters:
      l - the long to add.
      Returns:
      a BigFraction instance with the resulting values.

    • add

      public BigFraction add(BigFraction fraction)

      Adds the value of this fraction to another, returning the result in reduced form.

      Specified by:
      add in interface FieldElement<BigFraction>
      Parameters:
      fraction - the BigFraction to add, must not be null.
      Returns:
      a BigFraction instance with the resulting values.
      Throws:
      NullArgumentException - if the BigFraction is null.

    • bigDecimalValue

      public BigDecimal bigDecimalValue()

      Gets the fraction as a BigDecimal. This calculates the fraction as the 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:

    • bigDecimalValue

      public BigDecimal bigDecimalValue(RoundingMode roundingMode)

      Gets the fraction as a BigDecimal following the passed rounding mode. This calculates the fraction as the numerator divided by denominator.

      Parameters:
      roundingMode - rounding mode to apply. see BigDecimal constants.
      Returns:
      the fraction as a BigDecimal.
      Throws:
      IllegalArgumentException - if roundingMode does not represent a valid rounding mode.
      See Also:

    • bigDecimalValue

      public BigDecimal bigDecimalValue(int scale, RoundingMode roundingMode)

      Gets the fraction as a BigDecimal following the passed scale and rounding mode. This calculates the fraction as the numerator divided by denominator.

      Parameters:
      scale - scale of the BigDecimal quotient to be returned. see BigDecimal for more information.
      roundingMode - rounding mode to apply. see BigDecimal constants.
      Returns:
      the fraction as a BigDecimal.
      See Also:

    • compareTo

      public int compareTo(BigFraction object)

      Compares this object to another based on size.

      Specified by:
      compareTo in interface Comparable<BigFraction>
      Parameters:
      object - the object to compare to, must not be null.
      Returns:
      -1 if this is less than object, +1 if this is greater than object, 0 if they are equal.
      See Also:

    • divide

      public BigFraction divide(BigInteger bg)

      Divide the value of this fraction by the passed BigInteger, ie this * 1 / bg, returning the result in reduced form.

      Parameters:
      bg - the BigInteger to divide by, must not be null
      Returns:
      a BigFraction instance with the resulting values
      Throws:
      NullArgumentException - if the BigInteger is null
      MathRuntimeException - if the fraction to divide by is zero

    • divide

      public BigFraction divide(int i)

      Divide the value of this fraction by the passed int, ie this * 1 / i, returning the result in reduced form.

      Parameters:
      i - the int to divide by
      Returns:
      a BigFraction instance with the resulting values
      Throws:
      MathRuntimeException - if the fraction to divide by is zero

    • divide

      public BigFraction divide(long l)

      Divide the value of this fraction by the passed long, ie this * 1 / l, returning the result in reduced form.

      Parameters:
      l - the long to divide by
      Returns:
      a BigFraction instance with the resulting values
      Throws:
      MathRuntimeException - if the fraction to divide by is zero

    • divide

      public BigFraction divide(BigFraction fraction)

      Divide the value of this fraction by another, returning the result in reduced form.

      Specified by:
      divide in interface FieldElement<BigFraction>
      Parameters:
      fraction - Fraction to divide by, must not be null.
      Returns:
      a BigFraction instance with the resulting values.
      Throws:
      NullArgumentException - if the fraction is null.
      MathRuntimeException - if the fraction to divide by is zero

    • 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
      See Also:

    • equals

      public boolean equals(Object other)

      Test for the equality of two fractions. If the lowest term numerator and denominators are the same for both fractions, the two fractions are considered to be equal.

      Overrides:
      equals in class Object
      Parameters:
      other - fraction to test for equality to this fraction, can be null.
      Returns:
      true if two fractions are equal, false if object is null, not an instance of BigFraction, or not equal to this fraction instance.
      See Also:

    • 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.
      See Also:

    • gcd

      public BigFraction gcd(BigFraction s)
      Rational number greatest common divisor.
      Parameters:
      s - fraction.
      Returns:
      gcd(this, s).
      Since:
      3.1

    • lcm

      public BigFraction lcm(BigFraction s)
      Rational number least common multiple.
      Parameters:
      s - fraction.
      Returns:
      lcm(this, s).
      Since:
      3.1

    • getDenominator

      public BigInteger getDenominator()

      Access the denominator as a BigInteger.

      Returns:
      the denominator as a BigInteger.

    • getDenominatorAsInt

      public int getDenominatorAsInt()

      Access the denominator as a int.

      Returns:
      the denominator as a int.

    • getDenominatorAsLong

      public long getDenominatorAsLong()

      Access the denominator as a long.

      Returns:
      the denominator as a long.

    • getNumerator

      public BigInteger getNumerator()

      Access the numerator as a BigInteger.

      Returns:
      the numerator as a BigInteger.

    • getNumeratorAsInt

      public int getNumeratorAsInt()

      Access the numerator as a int.

      Returns:
      the numerator as a int.

    • getNumeratorAsLong

      public long getNumeratorAsLong()

      Access the numerator as a long.

      Returns:
      the numerator as a long.

    • hashCode

      public int hashCode()

      Gets a hashCode for the fraction.

      Overrides:
      hashCode in class Object
      Returns:
      a hash code value for this object.
      See Also:

    • 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.
      See Also:

    • 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.
      See Also:

    • multiply

      public BigFraction multiply(BigInteger bg)

      Multiplies the value of this fraction by the passed BigInteger, returning the result in reduced form.

      Parameters:
      bg - the BigInteger to multiply by.
      Returns:
      a BigFraction instance with the resulting values.
      Throws:
      NullArgumentException - if bg is null.

    • multiply

      public BigFraction multiply(int i)

      Multiply the value of this fraction by the passed int, returning the result in reduced form.

      Specified by:
      multiply in interface FieldElement<BigFraction>
      Parameters:
      i - the int to multiply by.
      Returns:
      a BigFraction instance with the resulting values.

    • multiply

      public BigFraction multiply(long l)

      Multiply the value of this fraction by the passed long, returning the result in reduced form.

      Parameters:
      l - the long to multiply by.
      Returns:
      a BigFraction instance with the resulting values.

    • multiply

      public BigFraction multiply(BigFraction fraction)

      Multiplies the value of this fraction by another, returning the result in reduced form.

      Specified by:
      multiply in interface FieldElement<BigFraction>
      Parameters:
      fraction - Fraction to multiply by, must not be null.
      Returns:
      a BigFraction instance with the resulting values.
      Throws:
      NullArgumentException - if fraction is null.

    • negate

      public BigFraction negate()

      Return the additive inverse of this fraction, returning the result in reduced form.

      Specified by:
      negate in interface FieldElement<BigFraction>
      Returns:
      the negation of this fraction.

    • percentageValue

      public double percentageValue()

      Gets the fraction percentage as a double. This calculates the fraction as the numerator divided by denominator multiplied by 100.

      Returns:
      the fraction percentage as a double.

    • pow

      public BigFraction pow(int exponent)

      Returns a BigFraction whose value is (this<sup>exponent</sup>), returning the result in reduced form.

      Parameters:
      exponent - exponent to which this BigFraction is to be raised.
      Returns:
      thisexponent

    • pow

      public BigFraction pow(long exponent)

      Returns a BigFraction whose value is thisexponent, returning the result in reduced form.

      Parameters:
      exponent - exponent to which this BigFraction is to be raised.
      Returns:
      thisexponent as a BigFraction.

    • pow

      public BigFraction pow(BigInteger exponent)

      Returns a BigFraction whose value is thisexponent, returning the result in reduced form.

      Parameters:
      exponent - exponent to which this BigFraction is to be raised.
      Returns:
      thisexponent as a BigFraction.

    • pow

      public double pow(double exponent)

      Returns a double whose value is thisexponent, returning the result in reduced form.

      Parameters:
      exponent - exponent to which this BigFraction is to be raised.
      Returns:
      thisexponent

    • reciprocal

      public BigFraction reciprocal()

      Return the multiplicative inverse of this fraction.

      Specified by:
      reciprocal in interface FieldElement<BigFraction>
      Returns:
      the reciprocal fraction.

    • reduce

      public BigFraction reduce()

      Reduce this BigFraction to its lowest terms.

      Returns:
      the reduced BigFraction. It doesn't change anything if the fraction can be reduced.

    • subtract

      public BigFraction subtract(BigInteger bg)

      Subtracts the value of an BigInteger from the value of this BigFraction, returning the result in reduced form.

      Parameters:
      bg - the BigInteger to subtract, cannot be null.
      Returns:
      a BigFraction instance with the resulting values.
      Throws:
      NullArgumentException - if the BigInteger is null.

    • subtract

      public BigFraction subtract(int i)

      Subtracts the value of an integer from the value of this BigFraction, returning the result in reduced form.

      Parameters:
      i - the integer to subtract.
      Returns:
      a BigFraction instance with the resulting values.

    • subtract

      public BigFraction subtract(long l)

      Subtracts the value of a long from the value of this BigFraction, returning the result in reduced form.

      Parameters:
      l - the long to subtract.
      Returns:
      a BigFraction instance with the resulting values.

    • subtract

      public BigFraction subtract(BigFraction fraction)

      Subtracts the value of another fraction from the value of this one, returning the result in reduced form.

      Specified by:
      subtract in interface FieldElement<BigFraction>
      Parameters:
      fraction - BigFraction to subtract, must not be null.
      Returns:
      a BigFraction instance with the resulting values
      Throws:
      NullArgumentException - if the fraction is null.

    • toString

      public String toString()

      Returns the String representing this fraction, ie "num / dem" or just "num" if the denominator is one.

      Overrides:
      toString in class Object
      Returns:
      a string representation of the fraction.
      See Also:

    • getField

      public BigFractionField getField()
      Get the Field to which the instance belongs.
      Specified by:
      getField in interface FieldElement<BigFraction>
      Returns:
      Field to which the instance belongs