Package org.apache.commons.numbers.fraction

Class BigFraction

java.lang.Object

java.lang.Number

org.apache.commons.numbers.fraction.BigFraction

All Implemented Interfaces:

java.io.Serializable, java.lang.Comparable<BigFraction>, Addition<BigFraction>, Multiplication<BigFraction>, NativeOperators<BigFraction>

public final class BigFraction
extends java.lang.Number
implements java.lang.Comparable<BigFraction>, NativeOperators<BigFraction>, java.io.Serializable

Representation of a rational number using arbitrary precision.

The number is expressed as the quotient p/q of two BigIntegers, a numerator p and a non-zero denominator q.

This class is immutable. Rational number

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
private static int	DEFAULT_MAX_ITERATIONS	The default iterations used for convergence.
private java.math.BigInteger	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 java.math.BigInteger	numerator	The numerator of this fraction reduced to lowest terms.
static BigFraction	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 BigFraction	ZERO	A fraction representing "0".

Constructor Summary

Constructors

Modifier	Constructor	Description
private	BigFraction(java.math.BigInteger num)	Private constructor: Instances are created using factory methods.
private	BigFraction(java.math.BigInteger num, java.math.BigInteger den)	Private constructor: Instances are created using factory methods.

Method Summary

Modifier and Type	Method	Description
BigFraction	abs()	Returns the absolute value of this fraction.
BigFraction	add(int value)	Adds the specified value to this fraction, returning the result in reduced form.
BigFraction	add(long value)	Adds the specified value to this fraction, returning the result in reduced form.
BigFraction	add(java.math.BigInteger value)	Adds the specified value to this fraction, returning the result in reduced form.
BigFraction	add(BigFraction value)	Adds the specified value to this fraction, returning the result in reduced form.
java.math.BigDecimal	bigDecimalValue()	Returns the BigDecimal representation of this fraction.
java.math.BigDecimal	bigDecimalValue(int scale, java.math.RoundingMode roundingMode)	Returns the BigDecimal representation of this fraction.
java.math.BigDecimal	bigDecimalValue(java.math.RoundingMode roundingMode)	Returns the BigDecimal representation of this fraction.
int	compareTo(BigFraction other)	Compares this object with the specified object for order using the signed magnitude.
BigFraction	divide(int value)	Divide this fraction by the passed value, returning the result in reduced form.
BigFraction	divide(long value)	Divide this fraction by the passed value, returning the result in reduced form.
BigFraction	divide(java.math.BigInteger value)	Divide this fraction by the passed value, returning the result in reduced form.
BigFraction	divide(BigFraction 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 BigFraction	from(double value)	Create a fraction given the double value.
static BigFraction	from(double value, double epsilon, int maxIterations)	Create a fraction given the double value and maximum error allowed.
private static BigFraction	from(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.
static BigFraction	from(double value, int maxDenominator)	Create a fraction given the double value and maximum denominator.
java.math.BigInteger	getDenominator()	Access the denominator as a BigInteger.
int	getDenominatorAsInt()	Access the denominator as an int.
long	getDenominatorAsLong()	Access the denominator as a long.
java.math.BigInteger	getNumerator()	Access the numerator as a BigInteger.
int	getNumeratorAsInt()	Access the numerator as an int.
long	getNumeratorAsLong()	Access the numerator as a long.
int	hashCode()
int	intValue()	Returns the whole number part of the fraction.
boolean	isOne()	Check if this is a neutral element of multiplication, i.e.
boolean	isZero()	Check if this is a neutral element of addition, i.e.
long	longValue()	Returns the whole number part of the fraction.
BigFraction	multiply(int value)	Multiply this fraction by the passed value, returning the result in reduced form.
BigFraction	multiply(long value)	Multiply this fraction by the passed value, returning the result in reduced form.
BigFraction	multiply(java.math.BigInteger value)	Multiply this fraction by the passed value, returning the result in reduced form.
BigFraction	multiply(BigFraction value)	Multiply this fraction by the passed value, returning the result in reduced form.
BigFraction	negate()	Additive inverse.
static BigFraction	of(int num)	Create a fraction given the numerator.
static BigFraction	of(int num, int den)	Create a fraction given the numerator and denominator.
static BigFraction	of(long num)	Create a fraction given the numerator.
static BigFraction	of(long num, long den)	Create a fraction given the numerator and denominator.
static BigFraction	of(java.math.BigInteger num)	Create a fraction given the numerator.
static BigFraction	of(java.math.BigInteger num, java.math.BigInteger den)	Create a fraction given the numerator and denominator.
BigFraction	one()	Identity element.
static BigFraction	parse(java.lang.String s)	Returns a BigFraction instance representing the specified string s.
BigFraction	pow(int exponent)	Returns a BigFraction whose value is thisexponent, returning the result in reduced form.
BigFraction	reciprocal()	Multiplicative inverse.
private static java.math.BigInteger	roundAndRightShift(java.math.BigInteger value, int bits, boolean hasFractionalBits)	Rounds an integer to the specified power of two (i.e.
int	signum()	Retrieves the sign of this fraction.
BigFraction	subtract(int value)	Subtracts the specified value from this fraction, returning the result in reduced form.
BigFraction	subtract(long value)	Subtracts the specified value from this fraction, returning the result in reduced form.
BigFraction	subtract(java.math.BigInteger value)	Subtracts the specified value from this fraction, returning the result in reduced form.
BigFraction	subtract(BigFraction value)	Subtracts the specified value from this fraction, returning the result in reduced form.
private long	toFloatingPointBits(int exponentLength, int significandLength)	Calculates the sign bit, the biased exponent and the significand for a binary floating-point representation of this BigFraction according to the IEEE 754 standard, and encodes these values into a long variable.
java.lang.String	toString()	Returns the String representing this fraction.
BigFraction	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 BigFraction ZERO

A fraction representing "0".

ONE

public static final BigFraction ONE

A fraction representing "1".

serialVersionUID

private static final long serialVersionUID

Serializable version identifier.

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 java.math.BigInteger numerator

The numerator of this fraction reduced to lowest terms.

denominator

private final java.math.BigInteger denominator

The denominator of this fraction reduced to lowest terms.

Constructor Detail

BigFraction

private BigFraction(java.math.BigInteger num,
                    java.math.BigInteger 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, must not be null.

den - Denominator, must not be null.

Throws:

java.lang.ArithmeticException - if the denominator is zero.

BigFraction

private BigFraction(java.math.BigInteger num)

Private constructor: Instances are created using factory methods.

This sets the denominator to 1.

Parameters:

num - Numerator (must not be null).

Method Detail

from

private static BigFraction from(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 method 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

Parameters:

value - Value to convert to a fraction.

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.

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 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:

java.lang.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:

• Continued Fraction equations (11) and (22)-(26)

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 BigFraction from(double value,
                               int maxDenominator)

Create a fraction given the double value and maximum denominator.

References:

• Continued Fraction equations (11) and (22)-(26)

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 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(java.math.BigInteger num)

Create a fraction given the numerator. The denominator is 1.

Parameters:

num - Numerator.

Returns:

a new instance.

Throws:

java.lang.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:

java.lang.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:

java.lang.ArithmeticException - if den is zero.

of

public static BigFraction of(java.math.BigInteger num,
                             java.math.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:

java.lang.NullPointerException - if numerator or denominator are null.

java.lang.ArithmeticException - if the denominator is zero.

parse

public static BigFraction parse(java.lang.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:

java.lang.NullPointerException - if the string is null.

java.lang.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()

one

public BigFraction one()

Description copied from interface: Multiplication

Identity element.

Specified by:

one in interface Multiplication<BigFraction>

Returns:

the field element such that for all a, one().multiply(a).equals(a) is true.

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 java.math.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 java.math.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.

negate

public BigFraction negate()

Description copied from interface: Addition

Additive inverse.

Specified by:

negate in interface Addition<BigFraction>

Returns:

-this.

reciprocal

public BigFraction reciprocal()

Multiplicative inverse.

Raises an exception if the fraction is equal to zero.

Specified by:

reciprocal in interface Multiplication<BigFraction>

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.

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.

Specified by:

floatValue in class java.lang.Number

Returns:

the fraction as a double.

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.

bigDecimalValue

public java.math.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:

java.lang.ArithmeticException - if the exact quotient does not have a terminating decimal expansion.

See Also:

BigDecimal

bigDecimalValue

public java.math.BigDecimal bigDecimalValue(java.math.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 java.math.BigDecimal bigDecimalValue(int scale,
                                            java.math.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:

java.lang.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(java.math.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(java.math.BigInteger 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(BigFraction value)

Subtracts the specified value from this fraction, returning the result in reduced form.

Specified by:

subtract in interface NativeOperators<BigFraction>

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(java.math.BigInteger 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(BigFraction value)

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

Specified by:

multiply in interface Multiplication<BigFraction>

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:

java.lang.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:

java.lang.ArithmeticException - if the value to divide by is zero

divide

public BigFraction divide(java.math.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:

java.lang.ArithmeticException - if the value to divide by is zero

divide

public BigFraction divide(BigFraction value)

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

Specified by:

divide in interface NativeOperators<BigFraction>

Parameters:

value - Value to divide by

Returns:

this / value.

Throws:

java.lang.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:

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(BigFraction other)

Compares this object with the specified object for order using the signed magnitude.

Specified by:

compareTo in interface java.lang.Comparable<BigFraction>

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

toFloatingPointBits

private long toFloatingPointBits(int exponentLength,
                                 int significandLength)

Calculates the sign bit, the biased exponent and the significand for a binary floating-point representation of this BigFraction according to the IEEE 754 standard, and encodes these values into a long variable. The representative bits are arranged adjacent to each other and placed at the low-order end of the returned long value, with the least significant bits used for the significand, the next more significant bits for the exponent, and next more significant bit for the sign.

Warning: The arguments are not validated.

Parameters:

exponentLength - the number of bits allowed for the exponent; must be between 1 and 32 (inclusive), and must not be greater than 63 - significandLength

significandLength - the number of bits allowed for the significand (excluding the implicit leading 1-bit in normalized numbers, e.g. 52 for a double-precision floating-point number); must be between 1 and 63 - exponentLength (inclusive)

Returns:

the bits of an IEEE 754 binary floating-point representation of this fraction encoded in a long, as described above.

roundAndRightShift

private static java.math.BigInteger roundAndRightShift(java.math.BigInteger value,
                                                       int bits,
                                                       boolean hasFractionalBits)

Rounds an integer to the specified power of two (i.e. the minimum number of low-order bits that must be zero) and performs a right-shift by this amount. The rounding mode applied is round to nearest, with ties rounding to even (meaning the prospective least significant bit must be zero). The number can optionally be treated as though it contained at least one 0-bit and one 1-bit in its fractional part, to influence the result in cases that would otherwise be a tie.

Parameters:

value - the number to round and right-shift

bits - the power of two to which to round; must be positive

hasFractionalBits - whether the number should be treated as though it contained a non-zero fractional part

Returns:

a BigInteger as described above