Package org.apfloat

Class Aprational

java.lang.Object

java.lang.Number

org.apfloat.Apcomplex

org.apfloat.Apfloat

org.apfloat.Aprational

All Implemented Interfaces:

Serializable, Comparable<Apfloat>, Formattable

Direct Known Subclasses:

Apint

public class Aprational
extends Apfloat

Arbitrary precision rational number class. An aprational consists of a numerator and a denominator of type Apint.

Version:

1.10.0

Author:

Mikko Tommila

See Also:

• Apint
• AprationalMath
• Serialized Form

Field Summary

Fields inherited from class org.apfloat.Apcomplex

DEFAULT, I, INFINITE, ONE, REAL_ABS_IMAG_ORDER, REAL_IMAG_ORDER, ZERO

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	Aprational()	Default constructor.
	Aprational(double value)	Constructs an aprational from a double.
	Aprational(double value, int radix)	Constructs an aprational from a double using the specified radix.
	Aprational(PushbackReader in)	Reads an aprational from a reader.
	Aprational(PushbackReader in, int radix)	Reads an aprational from a reader.
	Aprational(String value)	Constructs an aprational from a string.
	Aprational(String value, int radix)	Constructs an aprational from a string with the specified radix.
	Aprational(BigInteger value)	Constructs an aprational from a BigInteger.
	Aprational(BigInteger value, int radix)	Constructs an aprational from a BigInteger using the specified radix.
	Aprational(Apint value)	Construct an integer aprational whose denominator is one.
	Aprational(Apint numerator, Apint denominator)	Construct an aprational with the specified numerator and denominator.

Method Summary

Modifier and Type	Method	Description
Aprational	add(Aprational x)	Adds two aprational numbers.
Apint	ceil()	Ceiling function.
int	compareTo(Apfloat x)	Compare this aprational to the specified apfloat.
int	compareTo(Aprational x)	Compare this aprational to the specified aprational.
Apint	denominator()	Denominator of this aprational.
Aprational	divide(Aprational x)	Divides two aprational numbers.
boolean	equals(Object obj)	Compares this object to the specified object.
Apint	floor()	Floor function.
void	formatTo(Formatter formatter, int flags, int width, int precision)	Formats the object using the provided formatter.
Aprational	frac()	Returns the fractional part.
protected ApfloatImpl	getImpl(long precision)	Returns an ApfloatImpl representing the approximation of this aprational up to the requested precision.
int	hashCode()	Returns a hash code for this aprational.
boolean	isInteger()	Returns if this number has an integer value.
boolean	isShort()	Returns if this aprational is "short".
Aprational	mod(Aprational x)	Calculates the remainder when divided by an aprational.
Aprational	multiply(Aprational x)	Multiplies two aprational numbers.
Aprational	negate()	Negative value.
Apint	numerator()	Numerator of this aprational.
long	precision()	Returns the precision of this aprational.
boolean	preferCompare(Apfloat x)	Tests if the comparison with equals and compareTo should be done in the opposite order.
int	radix()	Radix of this aprational.
long	scale()	Returns the scale of this aprational.
int	signum()	Returns the signum function of this aprational.
long	size()	Returns the size of this aprational.
Aprational	subtract(Aprational x)	Subtracts two aprational numbers.
boolean	test(Apfloat x)	Tests two apfloat numbers for equality.
boolean	test(Aprational x)	Tests two aprational numbers for equality.
Aprational	toRadix(int radix)	Convert this aprational to the specified radix.
String	toString()	Returns a string representation of this aprational.
String	toString(boolean pretty)	Returns a string representation of this aprational.
Apint	truncate()	Truncates fractional part.
void	writeTo(Writer out)	Write a string representation of this aprational to a Writer.
void	writeTo(Writer out, boolean pretty)	Write a string representation of this aprational to a Writer.

Methods inherited from class org.apfloat.Apfloat

add, byteValue, divide, doubleValue, equalDigits, floatValue, imag, intValue, longValue, longValueExact, mod, multiply, precision, real, shortValue, subtract

Methods inherited from class org.apfloat.Apcomplex

add, byteValueExact, conj, divide, equalDigits, intValueExact, isZero, multiply, shortValueExact, subtract, test

Methods inherited from class java.lang.Object

clone, finalize, getClass, notify, notifyAll, wait, wait, wait

Constructor Details

Aprational

protected Aprational()

Default constructor. To be used only by subclasses that overload all needed methods.

Aprational

public Aprational(Apint value)
           throws ApfloatRuntimeException

Construct an integer aprational whose denominator is one.

Parameters:

value - The numerator of the number.

Throws:

ApfloatRuntimeException

Aprational

public Aprational(Apint numerator,
 Apint denominator)
           throws IllegalArgumentException,
ApfloatRuntimeException

Construct an aprational with the specified numerator and denominator.

Parameters:

numerator - The numerator.

denominator - The denominator.

Throws:

IllegalArgumentException - In case the denominator is zero, or if the denominator is not one or the numerator is not zero, and the radix of the numerator and denominator are different.

ApfloatRuntimeException

Aprational

public Aprational(String value)
           throws NumberFormatException,
IllegalArgumentException,
ApfloatRuntimeException

Constructs an aprational from a string. The default radix is used.

The input must be of one of the formats

integer
numerator [whitespace] "/" [whitespace] denominator

Parameters:

value - The input string.

Throws:

NumberFormatException - In case the number is invalid.

IllegalArgumentException - In case the denominator is zero.

ApfloatRuntimeException

Aprational

public Aprational(String value,
 int radix)
           throws NumberFormatException,
IllegalArgumentException,
ApfloatRuntimeException

Constructs an aprational from a string with the specified radix.

The input must be of one of the formats

integer
numerator [whitespace] "/" [whitespace] denominator

Parameters:

value - The input string.

radix - The radix to be used.

Throws:

NumberFormatException - In case the number is invalid.

IllegalArgumentException - In case the denominator is zero.

ApfloatRuntimeException

Aprational

public Aprational(PushbackReader in)
           throws IOException,
NumberFormatException,
IllegalArgumentException,
ApfloatRuntimeException

Reads an aprational from a reader. The default radix is used. The constructor stops reading at the first character it doesn't understand. The reader must thus be a PushbackReader so that the invalid character can be returned back to the stream.

The input must be of one of the formats

integer [whitespace]
numerator [whitespace] "/" [whitespace] denominator

Parameters:

in - The input stream.

Throws:

IOException - In case of I/O error reading the stream.

NumberFormatException - In case the number is invalid.

IllegalArgumentException - In case the denominator is zero.

ApfloatRuntimeException

Aprational

public Aprational(PushbackReader in,
 int radix)
           throws IOException,
NumberFormatException,
IllegalArgumentException,
ApfloatRuntimeException

Reads an aprational from a reader. The specified radix is used.

Parameters:

in - The input stream.

radix - The radix to be used.

Throws:

IOException - In case of I/O error reading the stream.

NumberFormatException - In case the number is invalid.

IllegalArgumentException - In case the denominator is zero.

ApfloatRuntimeException

See Also:

• Aprational(PushbackReader)

Aprational

public Aprational(BigInteger value)
           throws ApfloatRuntimeException

Constructs an aprational from a BigInteger. The default radix is used.

Parameters:

value - The numerator of the number.

Throws:

ApfloatRuntimeException

Aprational

public Aprational(BigInteger value,
 int radix)
           throws ApfloatRuntimeException

Constructs an aprational from a BigInteger using the specified radix.

Parameters:

value - The numerator of the number.

radix - The radix of the number.

Throws:

ApfloatRuntimeException

Aprational

public Aprational(double value)
           throws ApfloatRuntimeException

Constructs an aprational from a double. The exact value represented by the double is used. The default radix is used.

Note that doubles are presented as an integer multiplied by a power of two (positive or negative). Many numbers can't be represented exactly this way, e.g. new Aprational(0.1) won't result in 1/10 but in 3602879701896397/36028797018963968.

Parameters:

value - The numerator of the number.

Throws:

ApfloatRuntimeException

Aprational

public Aprational(double value,
 int radix)
           throws ApfloatRuntimeException

Constructs an aprational from a double using the specified radix. The exact value represented by the double is used.

Note that doubles are presented as an integer multiplied by a power of two (positive or negative). Many numbers can't be represented exactly this way, e.g. new Aprational(0.1) won't result in 1/10 but in 3602879701896397/36028797018963968.

Parameters:

value - The numerator of the number.

radix - The radix of the number.

Throws:

ApfloatRuntimeException

Method Details

numerator

public Apint numerator()

Numerator of this aprational.

Returns:

n where this = n / m.

denominator

public Apint denominator()

Denominator of this aprational.

Returns:

m where this = n / m.

radix

public int radix()

Radix of this aprational.

Overrides:

radix in class Apfloat

Returns:

Radix of this aprational.

precision

public long precision()
               throws ApfloatRuntimeException

Returns the precision of this aprational.

Overrides:

precision in class Apfloat

Returns:

INFINITE

Throws:

ApfloatRuntimeException

scale

public long scale()
           throws ApfloatRuntimeException

Returns the scale of this aprational. Scale is equal to the number of digits in the aprational's truncated value.

Zero has a scale of -INFINITE.

Overrides:

scale in class Apfloat

Returns:

Number of digits in the truncated value of this aprational in the radix in which it's presented.

Throws:

ApfloatRuntimeException

See Also:

• Apfloat.scale()

size

public long size()
          throws ApfloatRuntimeException

Returns the size of this aprational. Size is equal to the number of significant digits in the aprational's floating-point expansion. If the expansion is infinite then this method returns INFINITE.

Zero has a size of 0.

Overrides:

size in class Apfloat

Returns:

Number of significant digits in the floating-point expansion of this aprational in the radix in which it's presented.

Throws:

ApfloatRuntimeException

Since:

1.6

See Also:

• Apfloat.size()

signum

public int signum()

Returns the signum function of this aprational.

Overrides:

signum in class Apfloat

Returns:

-1, 0 or 1 as the value of this aprational is negative, zero or positive.

isShort

public boolean isShort()
                throws ApfloatRuntimeException

Returns if this aprational is "short".

Overrides:

isShort in class Apfloat

Returns:

true if the aprational is "short", false if not.

Throws:

ApfloatRuntimeException

See Also:

• Apfloat.isShort()

isInteger

public boolean isInteger()
                  throws ApfloatRuntimeException

Returns if this number has an integer value. Note that this does not necessarily mean that this object is an instance of Apint.

A rational number is an integer if the denominator is one.

Overrides:

isInteger in class Apfloat

Returns:

If this number's value is an integer.

Throws:

ApfloatRuntimeException

Since:

1.9.0

negate

public Aprational negate()
                  throws ApfloatRuntimeException

Negative value.

Overrides:

negate in class Apfloat

Returns:

-this.

Throws:

ApfloatRuntimeException

Since:

1.1

add

public Aprational add(Aprational x)
               throws ApfloatRuntimeException

Adds two aprational numbers.

Parameters:

x - The number to be added to this number.

Returns:

this + x.

Throws:

ApfloatRuntimeException

subtract

public Aprational subtract(Aprational x)
                    throws ApfloatRuntimeException

Subtracts two aprational numbers.

Parameters:

x - The number to be subtracted from this number.

Returns:

this - x.

Throws:

ApfloatRuntimeException

multiply

public Aprational multiply(Aprational x)
                    throws ApfloatRuntimeException

Multiplies two aprational numbers.

Parameters:

x - The number to be multiplied by this number.

Returns:

this * x.

Throws:

ApfloatRuntimeException

divide

public Aprational divide(Aprational x)
                  throws ArithmeticException,
ApfloatRuntimeException

Divides two aprational numbers.

Parameters:

x - The number by which this number is to be divided.

Returns:

this / x.

Throws:

ArithmeticException - In case the divisor is zero.

ApfloatRuntimeException

mod

public Aprational mod(Aprational x)
               throws ApfloatRuntimeException

Calculates the remainder when divided by an aprational. The result has the same sign as this number. If x is zero, then zero is returned.

Parameters:

x - The number that is used as the divisor in the remainder calculation.

Returns:

this % x.

Throws:

ApfloatRuntimeException

Since:

1.2

floor

public Apint floor()
            throws ApfloatRuntimeException

Floor function. Returns the largest (closest to positive infinity) value that is not greater than this aprational and is equal to a mathematical integer.

Overrides:

floor in class Apfloat

Returns:

This aprational rounded towards negative infinity.

Throws:

ApfloatRuntimeException

ceil

public Apint ceil()
           throws ApfloatRuntimeException

Ceiling function. Returns the smallest (closest to negative infinity) value that is not less than this aprational and is equal to a mathematical integer.

Overrides:

ceil in class Apfloat

Returns:

This aprational rounded towards positive infinity.

Throws:

ApfloatRuntimeException

truncate

public Apint truncate()
               throws ApfloatRuntimeException

Truncates fractional part.

Overrides:

truncate in class Apfloat

Returns:

This aprational rounded towards zero.

Throws:

ApfloatRuntimeException

frac

public Aprational frac()
                throws ApfloatRuntimeException

Returns the fractional part. The fractional part is always 0 <= abs(x.frac()) < 1. The fractional part has the same sign as the number. For the fractional and integer parts, this always holds:

x = x.truncate() + x.frac()

Overrides:

frac in class Apfloat

Returns:

The fractional part of this aprational.

Throws:

ApfloatRuntimeException

Since:

1.7.0

toRadix

public Aprational toRadix(int radix)
                   throws NumberFormatException,
ApfloatRuntimeException

Convert this aprational to the specified radix.

Overrides:

toRadix in class Apfloat

Parameters:

radix - The radix.

Returns:

This number in the specified radix.

Throws:

NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

Since:

1.2

compareTo

public int compareTo(Aprational x)

Compare this aprational to the specified aprational.

Parameters:

x - Aprational to which this aprational is to be compared.

Returns:

-1, 0 or 1 as this aprational is numerically less than, equal to, or greater than x.

compareTo

public int compareTo(Apfloat x)

Compare this aprational to the specified apfloat.

Specified by:

compareTo in interface Comparable<Apfloat>

Overrides:

compareTo in class Apfloat

Parameters:

x - Apfloat to which this aprational is to be compared.

Returns:

-1, 0 or 1 as this aprational is numerically less than, equal to, or greater than x.

preferCompare

public boolean preferCompare(Apfloat x)

Description copied from class: Apfloat

Tests if the comparison with equals and compareTo should be done in the opposite order.

Implementations should avoid infinite recursion.

Overrides:

preferCompare in class Apfloat

Parameters:

x - The number to compare to.

Returns:

true if this object should invoke x.equals(this) and -x.compareTo(this) instead of comparing normally.

equals

public boolean equals(Object obj)

Compares this object to the specified object.

Note: if two apfloats are compared where one number doesn't have enough precise digits, the mantissa is assumed to contain zeros. See Apfloat.compareTo(Apfloat).

Overrides:

equals in class Apfloat

Parameters:

obj - The object to compare with.

Returns:

true if the objects are the same; false otherwise.

test

public boolean test(Aprational x)

Tests two aprational numbers for equality. Returns false if the numbers are definitely known to be not equal. If true is returned, equality is unknown and should be verified by calling equals(Object). This method is usually significantly faster than calling equals(Object).

Parameters:

x - The number to test against.

Returns:

false if the numbers are definitely not equal, true if unknown.

Since:

1.10.0

test

public boolean test(Apfloat x)
             throws ApfloatRuntimeException

Description copied from class: Apfloat

Tests two apfloat numbers for equality. Returns false if the numbers are definitely known to be not equal. If true is returned, equality is unknown and should be verified by calling Apfloat.equals(Object). This method is usually significantly faster than calling equals(Object).

Overrides:

test in class Apfloat

Parameters:

x - The number to test against.

Returns:

false if the numbers are definitely not equal, true if unknown.

Throws:

ApfloatRuntimeException

hashCode

public int hashCode()

Returns a hash code for this aprational.

Overrides:

hashCode in class Apfloat

Returns:

The hash code value for this object.

toString

public String toString()

Returns a string representation of this aprational.

Overrides:

toString in class Apcomplex

Returns:

A string representing this object.

toString

public String toString(boolean pretty)
                throws ApfloatRuntimeException

Returns a string representation of this aprational.

Overrides:

toString in class Apfloat

Parameters:

pretty - true to use a fixed-point notation, false to use an exponential notation.

Returns:

A string representing this object.

Throws:

ApfloatRuntimeException

writeTo

public void writeTo(Writer out)
             throws IOException,
ApfloatRuntimeException

Write a string representation of this aprational to a Writer.

Overrides:

writeTo in class Apcomplex

Parameters:

out - The output Writer.

Throws:

IOException - In case of I/O error writing to the stream.

ApfloatRuntimeException

writeTo

public void writeTo(Writer out,
 boolean pretty)
             throws IOException,
ApfloatRuntimeException

Write a string representation of this aprational to a Writer.

Overrides:

writeTo in class Apfloat

Parameters:

out - The output Writer.

pretty - true to use a fixed-point notation, false to use an exponential notation.

Throws:

IOException - In case of I/O error writing to the stream.

ApfloatRuntimeException

formatTo

public void formatTo(Formatter formatter,
 int flags,
 int width,
 int precision)

Formats the object using the provided formatter.

Specified by:

formatTo in interface Formattable

Overrides:

formatTo in class Apfloat

Parameters:

formatter - The formatter.

flags - The flags to modify the output format.

width - The minimum number of characters to be written to the output, or -1 for no minimum.

precision - The maximum number of characters to be written to the output, or -1 for no maximum.

Since:

1.3

See Also:

• Apfloat.formatTo(Formatter,int,int,int)

getImpl

protected ApfloatImpl getImpl(long precision)
                       throws ApfloatRuntimeException

Returns an ApfloatImpl representing the approximation of this aprational up to the requested precision.

Overrides:

getImpl in class Apfloat

Parameters:

precision - Precision of the ApfloatImpl that is needed.

Returns:

An ApfloatImpl representing this object to the requested precision.

Throws:

ApfloatRuntimeException