Package org.apfloat

Class Apcomplex

java.lang.Object

java.lang.Number

org.apfloat.Apcomplex

All Implemented Interfaces:

Serializable, Formattable

Direct Known Subclasses:

Apfloat

public class Apcomplex
extends Number
implements Formattable, Serializable

Arbitrary precision complex number class. An apcomplex consists of a real and imaginary part of type Apfloat.

Note that although the Apcomplex class extends Number, the methods inherited from Number return the value of the real part of the complex number. Thus they are more meaningful for the Apfloat class and its subclasses.

Version:

1.13.0

Author:

Mikko Tommila

See Also:

• Apfloat
• ApcomplexMath
• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static final long	DEFAULT	Default precision.
static final Apcomplex	I	Imaginary unit.
static final long	INFINITE	Infinite precision or scale.
static final Apint	ONE	Constant for one.
static final Comparator<Apcomplex>	REAL_ABS_IMAG_ORDER	Comparator for ordering by real part, and in case of a tie, by the absolute value of the imaginary part.
static final Comparator<Apcomplex>	REAL_IMAG_ORDER	Comparator for ordering by real part, and in case of a tie, by imaginary part.
static final Apint	ZERO	Constant for zero.

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	Apcomplex()	Default constructor.
	Apcomplex(PushbackReader in)	Reads an apcomplex from a reader.
	Apcomplex(String value)	Constructs an apcomplex from a string.
	Apcomplex(Apfloat real)	Construct a real apcomplex whose imaginary part is zero.
	Apcomplex(Apfloat real, Apfloat imag)	Construct an apcomplex with the specified real and imaginary part.

Method Summary

Modifier and Type	Method	Description
Apcomplex	add(Apcomplex z)	Adds two apcomplex numbers.
byte	byteValue()	Returns the value of the this number as a byte.
byte	byteValueExact()	Returns the value of the this number as a byte, checking for lost information.
Apcomplex	conj()	Returns the complex conjugate of this apcomplex.
Apcomplex	divide(Apcomplex z)	Divides two apcomplex numbers.
double	doubleValue()	Returns the value of the this number as a double.
long	equalDigits(Apcomplex z)	Computes number of equal digits.
boolean	equals(Object obj)	Compares this object to the specified object.
float	floatValue()	Returns the value of the this number as a float.
void	formatTo(Formatter formatter, int flags, int width, int precision)	Formats the object using the provided formatter.
int	hashCode()	Returns a hash code for this apcomplex.
Apfloat	imag()	Returns the imaginary part of this apcomplex.
int	intValue()	Returns the value of the this number as an int.
int	intValueExact()	Returns the value of the this number as an int, checking for lost information.
boolean	isInteger()	Returns if this number has an integer value.
boolean	isZero()	Returns if this number is zero.
long	longValue()	Returns the value of the this number as a long.
long	longValueExact()	Returns the value of the this number as a long, checking for lost information.
Apcomplex	multiply(Apcomplex z)	Multiplies two apcomplex numbers.
Apcomplex	negate()	Negative value.
long	precision()	Returns the precision of this apcomplex.
Apcomplex	precision(long precision)	Returns an apcomplex with the same value as this apcomplex accurate to the specified precision.
int	radix()	Radix of this apcomplex.
Apfloat	real()	Returns the real part of this apcomplex.
long	scale()	Returns the scale of this apcomplex.
short	shortValue()	Returns the value of the this number as a short.
short	shortValueExact()	Returns the value of the this number as a short, checking for lost information.
long	size()	Returns the size of this apcomplex.
Apcomplex	subtract(Apcomplex z)	Subtracts two apcomplex numbers.
boolean	test(Apcomplex z)	Tests two apcomplex numbers for equality.
Apcomplex	toRadix(int radix)	Convert this apcomplex to the specified radix.
String	toString()	Returns a string representation of this apcomplex.
String	toString(boolean pretty)	Returns a string representation of this apcomplex.
void	writeTo(Writer out)	Write a string representation of this apcomplex to a Writer.
void	writeTo(Writer out, boolean pretty)	Write a string representation of this apcomplex to a Writer.

Methods inherited from class java.lang.Object

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

Field Details

ZERO

public static final Apint ZERO

Constant for zero. It is safe to use ZERO in all addition, subtraction, multiplication, division and comparison operations regardless of the radix used.

ONE

public static final Apint ONE

Constant for one. Note that this number is created using the initial default radix. It is safe to use ONE in all multiplication, division and equality comparison operations regardless of the radix used. However, in subtraction and addition it only works with numbers in the same radix.

I

public static final Apcomplex I

Imaginary unit. That is, Apcomplex(ZERO, ONE). It is safe to use I in all multiplication, division and equality comparison operations regardless of the radix used. In addition and subtraction it only works with numbers in the same radix.

INFINITE

public static final long INFINITE

Infinite precision or scale. Can be used as the precision argument when constructing apfloats.

See Also:

• Constant Field Values

DEFAULT

public static final long DEFAULT

Default precision. Can be used as an argument when constructing apfloats.

See Also:

• Constant Field Values

REAL_IMAG_ORDER

public static final Comparator<Apcomplex> REAL_IMAG_ORDER

Comparator for ordering by real part, and in case of a tie, by imaginary part.

REAL_ABS_IMAG_ORDER

public static final Comparator<Apcomplex> REAL_ABS_IMAG_ORDER

Comparator for ordering by real part, and in case of a tie, by the absolute value of the imaginary part. If a tie persists, order by imaginary part.

Constructor Details

Apcomplex

protected Apcomplex()

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

Apcomplex

public Apcomplex(Apfloat real)

Construct a real apcomplex whose imaginary part is zero.

Parameters:

real - The real part of the number.

Apcomplex

public Apcomplex(Apfloat real,
 Apfloat imag)
          throws IllegalArgumentException

Construct an apcomplex with the specified real and imaginary part.

Parameters:

real - The real part of the number.

imag - The imaginary part of the number.

Throws:

IllegalArgumentException - If the real part and imaginary part are not zero but have different radixes.

Apcomplex

public Apcomplex(String value)
          throws NumberFormatException,
ApfloatRuntimeException

Constructs an apcomplex from a string.

The input must be of one of the formats

realPart
"(" [whitespace] realPart [whitespace] ")"
"(" [whitespace] realPart [whitespace] "," [whitespace] imaginaryPart [whitespace] ")"

Parameters:

value - The input string.

Throws:

NumberFormatException - If the number is invalid.

ApfloatRuntimeException

Apcomplex

public Apcomplex(PushbackReader in)
          throws IOException,
NumberFormatException,
ApfloatRuntimeException

Reads an apcomplex from a reader. 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

realPart
"(" [whitespace] realPart [whitespace] ")"
"(" [whitespace] realPart [whitespace] "," [whitespace] imaginaryPart [whitespace] ")"

Parameters:

in - The input stream.

Throws:

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

NumberFormatException - If the number is invalid.

ApfloatRuntimeException

Method Details

radix

public int radix()

Radix of this apcomplex.

Returns:

Radix of this apcomplex.

real

public Apfloat real()

Returns the real part of this apcomplex.

Returns:

The real part of this apcomplex.

imag

public Apfloat imag()

Returns the imaginary part of this apcomplex.

Returns:

The imaginary part of this apcomplex.

conj

public Apcomplex conj()
               throws ApfloatRuntimeException

Returns the complex conjugate of this apcomplex.

Returns:

x - i y, where this apcomplex is x + i y.

Throws:

ApfloatRuntimeException

precision

public long precision()
               throws ApfloatRuntimeException

Returns the precision of this apcomplex.

Returns:

The precision of this apcomplex in number of digits of the radix in which it's presented.

Throws:

ApfloatRuntimeException

precision

public Apcomplex precision(long precision)
                    throws IllegalArgumentException,
ApfloatRuntimeException

Returns an apcomplex with the same value as this apcomplex accurate to the specified precision.

If the requested precision less than this number's current precision, the functionality is quite obvious: the precision is simply truncated, and e.g. comparison and equality checking will work as expected. Some rounding errors in e.g. addition and subtraction may still occur, as "invisible" trailing digits can remain in the number.

If the requested precision more than this number's current precision, the functionality is quite undefined: the digits up to this number's current precision are guaranteed to be the same, but the "new" digits are undefined: they may be zero, or they may be digits that have been previously discarded with a call to precision() with a smaller number of digits, or they may be something else, or any combination of these.

These limitations allow various performance optimizations to be made.

Parameters:

precision - Precision of the new apcomplex.

Returns:

An apcomplex with the specified precision and same value as this apcomplex.

Throws:

IllegalArgumentException - If precision is <= 0.

ApfloatRuntimeException

Since:

1.2

scale

public long scale()
           throws ApfloatRuntimeException

Returns the scale of this apcomplex. The scale is the maximum of the scale of the real part and imaginary part.

Zero has a scale of -INFINITE.

Returns:

The exponent of this apcomplex in number of digits of the radix in which it's presented.

Throws:

ApfloatRuntimeException

See Also:

• Apfloat.scale()

size

public long size()
          throws ApfloatRuntimeException

Returns the size of this apcomplex. The size is the maximum of the size of the real part and imaginary part.

Zero has a size of 0.

Returns:

The number of digits in this number, from the most significant digit to the least significant nonzero digit, in the radix in which it's presented.

Throws:

ApfloatRuntimeException

Since:

1.6

See Also:

• Apfloat.size()

isZero

public boolean isZero()
               throws ApfloatRuntimeException

Returns if this number is zero.

Returns:

If this number is zero.

Throws:

ApfloatRuntimeException

Since:

1.13.0

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. Neither does it mean that the precision is infinite.

A complex number needs to have a zero imaginary part to be an integer.

Returns:

If this number's value is an integer.

Throws:

ApfloatRuntimeException

Since:

1.9.0

negate

public Apcomplex negate()
                 throws ApfloatRuntimeException

Negative value.

Returns:

-this.

Throws:

ApfloatRuntimeException

Since:

1.1

add

public Apcomplex add(Apcomplex z)
              throws ApfloatRuntimeException

Adds two apcomplex numbers.

Parameters:

z - The number to be added to this number.

Returns:

this + z.

Throws:

ApfloatRuntimeException

subtract

public Apcomplex subtract(Apcomplex z)
                   throws ApfloatRuntimeException

Subtracts two apcomplex numbers.

Parameters:

z - The number to be subtracted from this number.

Returns:

this - z.

Throws:

ApfloatRuntimeException

multiply

public Apcomplex multiply(Apcomplex z)
                   throws ApfloatRuntimeException

Multiplies two apcomplex numbers.

Parameters:

z - The number to be multiplied by this number.

Returns:

this * z.

Throws:

ApfloatRuntimeException

divide

public Apcomplex divide(Apcomplex z)
                 throws ArithmeticException,
ApfloatRuntimeException

Divides two apcomplex numbers.

Parameters:

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

Returns:

this / z.

Throws:

ArithmeticException - In case the divisor is zero.

ApfloatRuntimeException

doubleValue

public double doubleValue()

Returns the value of the this number as a double. Only takes the real part of this number.

Specified by:

doubleValue in class Number

Returns:

The numeric value represented by this object after conversion to type double.

See Also:

• Apfloat.doubleValue()

floatValue

public float floatValue()

Returns the value of the this number as a float. Only takes the real part of this number.

Specified by:

floatValue in class Number

Returns:

The numeric value represented by this object after conversion to type float.

See Also:

• Apfloat.floatValue()

byteValue

public byte byteValue()

Returns the value of the this number as a byte. Only takes the real part of this number.

Overrides:

byteValue in class Number

Returns:

The numeric value represented by this object after conversion to type byte.

See Also:

• Apfloat.byteValue()

shortValue

public short shortValue()

Returns the value of the this number as a short. Only takes the real part of this number.

Overrides:

shortValue in class Number

Returns:

The numeric value represented by this object after conversion to type short.

See Also:

• Apfloat.shortValue()

intValue

public int intValue()

Returns the value of the this number as an int. Only takes the real part of this number.

Specified by:

intValue in class Number

Returns:

The numeric value represented by this object after conversion to type int.

See Also:

• Apfloat.intValue()

longValue

public long longValue()

Returns the value of the this number as a long. Only takes the real part of this number.

Specified by:

longValue in class Number

Returns:

The numeric value represented by this object after conversion to type long.

See Also:

• Apfloat.longValue()

byteValueExact

public byte byteValueExact()
                    throws ArithmeticException

Returns the value of the this number as a byte, checking for lost information. If the value of this number is out of the range of the byte type, then an ArithmeticException is thrown.

Returns:

The numeric value represented by this object after conversion to type byte.

Throws:

ArithmeticException - If the value of this will not exactly fit in a byte or has a nonzero fractional part.

Since:

1.9.0

shortValueExact

public short shortValueExact()
                      throws ArithmeticException

Returns the value of the this number as a short, checking for lost information. If the value of this number is out of the range of the short type, then an ArithmeticException is thrown.

Returns:

The numeric value represented by this object after conversion to type short or has a nonzero fractional part.

Throws:

ArithmeticException - If the value of this will not exactly fit in a short.

Since:

1.9.0

intValueExact

public int intValueExact()
                  throws ArithmeticException

Returns the value of the this number as an int, checking for lost information. If the value of this number is out of the range of the int type, then an ArithmeticException is thrown.

Returns:

The numeric value represented by this object after conversion to type int.

Throws:

ArithmeticException - If the value of this will not exactly fit in an int or has a nonzero fractional part.

Since:

1.9.0

longValueExact

public long longValueExact()
                    throws ArithmeticException

Returns the value of the this number as a long, checking for lost information. If the value of this number is out of the range of the long type, then an ArithmeticException is thrown.

Returns:

The numeric value represented by this object after conversion to type long.

Throws:

ArithmeticException - If the value of this will not exactly fit in a long or has a nonzero fractional part.

Since:

1.9.0

equalDigits

public long equalDigits(Apcomplex z)
                 throws ApfloatRuntimeException

Computes number of equal digits.

Compares the digits of the numbers starting from the most significant digits. The exponent and sign are taken into consideration, so if either one doesn't match, the numbers are considered to have zero equal digits.

For example, the numbers (12345, 123) and (123456, 12) have zero matching digits, and the numbers (12345, 12) and (12355, 13) have three matching digits.

Parameters:

z - Number to compare with.

Returns:

Number of matching digits in the radix in which the numbers are presented.

Throws:

ApfloatRuntimeException

toRadix

public Apcomplex toRadix(int radix)
                  throws NumberFormatException,
ApfloatRuntimeException

Convert this apcomplex to the specified radix.

Parameters:

radix - The radix.

Returns:

This number in the specified radix.

Throws:

NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

Since:

1.2

equals

public boolean equals(Object obj)

Compares this object to the specified object.

Note: two apfloats are considered equal if they have an identical mantissa, but different precision.

Overrides:

equals in class Object

Parameters:

obj - The object to compare with.

Returns:

true if the objects are equal; false otherwise.

test

public boolean test(Apcomplex z)
             throws ApfloatRuntimeException

Tests two apcomplex 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:

z - The number to test against.

Returns:

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

Throws:

ApfloatRuntimeException

Since:

1.10.0

hashCode

public int hashCode()

Returns a hash code for this apcomplex.

Overrides:

hashCode in class Object

Returns:

The hash code value for this object.

toString

public String toString()

Returns a string representation of this apcomplex.

Overrides:

toString in class Object

Returns:

A string representing this object.

toString

public String toString(boolean pretty)
                throws ApfloatRuntimeException

Returns a string representation of this apcomplex.

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 apcomplex to a Writer.

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 apcomplex to a Writer.

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

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)