Class 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.
Since:
2.0
Serialized Form
• Field Summary

Fields
Modifier and Type Field Description
`static BigFraction` `FOUR_FIFTHS`
A fraction representing "4/5".
`static BigFraction` `MINUS_ONE`
A fraction representing "-1 / 1".
`static BigFraction` `ONE`
A fraction representing "1".
`static BigFraction` `ONE_FIFTH`
A fraction representing "1/5".
`static BigFraction` `ONE_HALF`
A fraction representing "1/2".
`static BigFraction` `ONE_QUARTER`
A fraction representing "1/4".
`static BigFraction` `ONE_THIRD`
A fraction representing "1/3".
`static BigFraction` `THREE_FIFTHS`
A fraction representing "3/5".
`static BigFraction` `THREE_QUARTERS`
A fraction representing "3/4".
`static BigFraction` `TWO`
A fraction representing "2 / 1".
`static BigFraction` `TWO_FIFTHS`
A fraction representing "2/5".
`static BigFraction` `TWO_QUARTERS`
A fraction representing "2/4".
`static BigFraction` `TWO_THIRDS`
A fraction representing "2/3".
`static BigFraction` `ZERO`
A fraction representing "0".
• Constructor Summary

Constructors
Constructor Description
`BigFraction​(double value)`
Create a fraction given the double value.
```BigFraction​(double value, double epsilon, int maxIterations)```
Create a fraction given the double value and maximum error allowed.
```BigFraction​(double value, int maxDenominator)```
Create a fraction given the double value and maximum denominator.
`BigFraction​(int num)`
Create a `BigFraction` equivalent to the passed int, ie "num / 1".
```BigFraction​(int num, int den)```
Create a `BigFraction` given the numerator and denominator as simple int.
`BigFraction​(long num)`
Create a `BigFraction` equivalent to the passed long, ie "num / 1".
```BigFraction​(long num, long den)```
Create a `BigFraction` given the numerator and denominator as simple long.
`BigFraction​(BigInteger num)`
Create a `BigFraction` equivalent to the passed BigInteger, ie "num / 1".
```BigFraction​(BigInteger num, BigInteger den)```
Create a `BigFraction` given the numerator and denominator as `BigInteger`.
• Method Summary

All Methods
Modifier and Type Method Description
`BigFraction` `abs()`
Returns the absolute value of this `BigFraction`.
`BigFraction` `add​(int i)`
Adds the value of this fraction to the passed integer, returning the result in reduced form.
`BigFraction` `add​(long l)`
Adds the value of this fraction to the passed long, returning the result in reduced form.
`BigFraction` `add​(BigInteger bg)`
Adds the value of this fraction to the passed `BigInteger`, returning the result in reduced form.
`BigFraction` `add​(BigFraction fraction)`
Adds the value of this fraction to another, returning the result in reduced form.
`BigDecimal` `bigDecimalValue()`
Gets the fraction as a `BigDecimal`.
`BigDecimal` `bigDecimalValue​(int roundingMode)`
Gets the fraction as a `BigDecimal` following the passed rounding mode.
`BigDecimal` ```bigDecimalValue​(int scale, int roundingMode)```
Gets the fraction as a `BigDecimal` following the passed scale and rounding mode.
`int` `compareTo​(BigFraction object)`
Compares this object to another based on size.
`BigFraction` `divide​(int i)`
Divide the value of this fraction by the passed int, ie "this * 1 / i", returning the result in reduced form.
`BigFraction` `divide​(long l)`
Divide the value of this fraction by the passed long, ie "this * 1 / l", returning the result in reduced form.
`BigFraction` `divide​(BigInteger bg)`
Divide the value of this fraction by the passed `BigInteger`, ie "this * 1 / bg", returning the result in reduced form.
`BigFraction` `divide​(BigFraction fraction)`
Divide the value of this fraction by another, returning the result in reduced form.
`double` `doubleValue()`
Gets the fraction as a double.
`boolean` `equals​(Object other)`
Test for the equality of two fractions.
`float` `floatValue()`
Gets the fraction as a float.
`BigInteger` `getDenominator()`
Access the denominator as a `BigInteger`.
`int` `getDenominatorAsInt()`
Access the denominator as a int.
`long` `getDenominatorAsLong()`
Access the denominator as a long.
`BigFractionField` `getField()`
Get the `Field` to which the instance belongs.
`BigInteger` `getNumerator()`
Access the numerator as a `BigInteger`.
`int` `getNumeratorAsInt()`
Access the numerator as a int.
`long` `getNumeratorAsLong()`
Access the numerator as a long.
`static BigFraction` ```getReducedFraction​(int numerator, int denominator)```
Creates a `BigFraction` instance with the 2 parts of a fraction Y/Z.
`int` `hashCode()`
Gets a hashCode for the fraction.
`int` `intValue()`
Gets the fraction as an int.
`long` `longValue()`
Gets the fraction as a long.
`BigFraction` `multiply​(int i)`
Multiply the value of this fraction by the passed int, returning the result in reduced form.
`BigFraction` `multiply​(long l)`
Multiply the value of this fraction by the passed long, returning the result in reduced form.
`BigFraction` `multiply​(BigInteger bg)`
Multiplies the value of this fraction by the passed `BigInteger`, returning the result in reduced form.
`BigFraction` `multiply​(BigFraction fraction)`
Multiplies the value of this fraction by another, returning the result in reduced form.
`BigFraction` `negate()`
Return the additive inverse of this fraction, returning the result in reduced form.
`double` `percentageValue()`
Gets the fraction percentage as a double.
`double` `pow​(double exponent)`
Returns a `double` whose value is (thisexponent), returning the result in reduced form.
`BigFraction` `pow​(int exponent)`
Returns a integer whose value is (thisexponent), returning the result in reduced form.
`BigFraction` `pow​(long exponent)`
Returns a `BigFraction` whose value is (thisexponent), returning the result in reduced form.
`BigFraction` `pow​(BigInteger exponent)`
Returns a `BigFraction` whose value is (thisexponent), returning the result in reduced form.
`BigFraction` `reciprocal()`
Return the multiplicative inverse of this fraction.
`BigFraction` `reduce()`
Reduce this `BigFraction` to its lowest terms.
`BigFraction` `subtract​(int i)`
Subtracts the value of an integer from the value of this one, returning the result in reduced form.
`BigFraction` `subtract​(long l)`
Subtracts the value of an integer from the value of this one, returning the result in reduced form.
`BigFraction` `subtract​(BigInteger bg)`
Subtracts the value of an `BigInteger` from the value of this one, returning the result in reduced form.
`BigFraction` `subtract​(BigFraction fraction)`
Subtracts the value of another fraction from the value of this one, returning the result in reduced form.
`String` `toString()`
Returns the `String` representing this fraction, ie "num / dem" or just "num" if the denominator is one.
• Methods inherited from class java.lang.Number

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

`getClass, notify, notifyAll, wait, wait, wait`
• Field Detail

• 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 Detail

• 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:
`ArithmeticException` - if the denominator is zero.
• BigFraction

```public BigFraction​(double value)
throws IllegalArgumentException```
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 does work 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:
`IllegalArgumentException` - if value is NaN or infinite
`BigFraction(double, double, int)`
• BigFraction

```public BigFraction​(double value,
double epsilon,
int maxIterations)
throws FractionConversionException```
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:
`FractionConversionException` - if the continued fraction failed to converge.
`BigFraction(double)`
• BigFraction

```public BigFraction​(double value,
int maxDenominator)
throws FractionConversionException```
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:
`FractionConversionException` - 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 Detail

• 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`.

`public BigFraction add​(BigInteger bg)`

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:
`NullPointerException` - if the `BigInteger` is `null`.

`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.

`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.

`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:
`NullPointerException` - 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.
`BigDecimal`
• bigDecimalValue

`public BigDecimal bigDecimalValue​(int 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.
`BigDecimal`
• bigDecimalValue

```public BigDecimal bigDecimalValue​(int scale,
int 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`.
`BigDecimal`
• 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.
`Comparable.compareTo(java.lang.Object)`
• 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:
`NullPointerException` - if the `BigInteger` is `null`.
`ArithmeticException` - 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:
`ArithmeticException` - 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:
`ArithmeticException` - 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:
`NullPointerException` - if the `fraction` is `null`.
`ArithmeticException` - 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
`Number.doubleValue()`
• 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.
`Object.equals(java.lang.Object)`
• 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.
`Number.floatValue()`
• 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.
`Object.hashCode()`
• 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.
`Number.intValue()`
• 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.
`Number.longValue()`
• 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:
`NullPointerException` - 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.

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:
`NullPointerException` - if `fraction` is `null`.
• negate

`public BigFraction negate()`

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

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 integer whose value is (thisexponent), returning the result in reduced form.

Parameters:
`exponent` - exponent to which this `BigInteger` 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.

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 one, returning the result in reduced form.

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

`public BigFraction subtract​(int i)`

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

Parameters:
`l` - the long to subtract.
Returns:
a `BigFraction` instance with the resulting values, or this object if the long is zero.
• 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:
`NullPointerException` - 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.
`Object.toString()`
`public BigFractionField getField()`
Get the `Field` to which the instance belongs.
`getField` in interface `FieldElement<BigFraction>`
`Field` to which the instance belongs