Package org.jscience.mathematics.number

Class Real

java.lang.Object

java.lang.Number

org.jscience.mathematics.number.Number<Real>

org.jscience.mathematics.number.Real

All Implemented Interfaces:

Serializable, Comparable<Real>, javolution.lang.Immutable, javolution.lang.Realtime, javolution.lang.ValueType, javolution.xml.XMLSerializable, Field<Real>, GroupAdditive<Real>, GroupMultiplicative<Real>, Ring<Real>, Structure<Real>

public final class Real
extends Number<Real>
implements Field<Real>

This class represents a real number of arbitrary precision with known/guaranteed uncertainty. A real number consists of a significand, a maximum error (on the significand value) and a decimal exponent: ((significand ± error) · 10exponent).

Reals number can be exact (e.g. integer values scaled by a power of ten). Exactness is maintained for Ring operations (e.g. addition, multiplication), but typically lost when a multiplicative inverse is calculated. The minimum precision used for exact numbers is set by setExactPrecision(int) (context local setting, default 19 digits).

The actual precision and accuracy of any real number is available and guaranteed (the true/exact value is always within the precision/accuracy range).

Operations on instances of this class are quite fast as information substantially below the precision level (aka noise) is not processed/stored. There is no limit on a real precision but precision degenerates (due to numeric errors) and calculations accelerate as more and more operations are performed.

Instances of this class can be utilized to find approximate solutions to linear equations using the Matrix class for which high-precision reals is often required, the primitive type double being not accurate enough to resolve equations when the matrix's size exceeds 100x100. Furthermore, even for small matrices the "qualified" result is indicative of possible system singularities.

See Also:

• Wikipedia: Real number
• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
static final Real	NaN	Holds a Not-a-Number instance (infinite error).
static final Real	ONE	Holds the exact ONE instance.
static final Real	ZERO	Holds the exact ZERO instance.

Method Summary

Modifier and Type	Method	Description
Real	abs()	Returns the absolute value of this real number.
boolean	approximates(Real that)	Indicates if this real approximates the one specified.
int	compareTo(Real that)	Compares two real numbers numerically.
Real	copy()	Returns a copy of this number allocated by the calling thread (possibly on the stack).
Real	divide(long divisor)	Returns this real number divided by the specified int divisor.
Real	divide(Real that)	Returns this real number divided by the one specified.
double	doubleValue()	Returns the value of this real number as a double.
boolean	equals(Object that)	Compares this real number against the specified object.
int	getAccuracy()	Returns the number of decimal digits guaranteed exact which appear to the right of the decimal point (absolute error).
int	getError()	Returns the maximum error (positive) on this real significand.
static int	getExactPrecision()	Returns the local minimum precision (number of exact digits) when exact numbers have to be approximated.
int	getExponent()	Returns the exponent of the power of 10 multiplier.
final int	getPrecision()	Returns the total number of decimal digits guaranteed exact (relative error).
LargeInteger	getSignificand()	Returns this real significand value.
int	hashCode()	Returns the hash code for this real number.
Real	inverse()	Returns the reciprocal (or inverse) of this real number.
boolean	isExact()	Indicates if this real number is exact (error == 0).
boolean	isLargerThan(Real that)	Compares the absolute value of two real numbers.
boolean	isNaN()	Indicates if this real is Not-a-Number (unbounded value interval).
boolean	isNegative()	Indicates if this real is less than zero.
boolean	isPositive()	Indicates if this real is greater than zero.
long	longValue()	Returns the value of this real number as a long.
Real	minus(Real that)	Returns the difference between this real number and the one specified.
Real	opposite()	Returns the negation of this real number.
Real	plus(Real that)	Returns the sum of this real number with the one specified.
LargeInteger	round()	Returns the closest integer value to this rational number.
static void	setExactPrecision(int precision)	Sets the local minimum precision (number of exact digits) when exact numbers have to be approximated.
Real	sqrt()	Returns the square root of this real number, the more accurate is this real number, the more accurate the square root.
Real	times(long multiplier)	Returns the product of this real number with the specified long multiplier.
Real	times(Real that)	Returns the product of this real number with the one specified.
javolution.text.Text	toText()	Returns the decimal text representation of this number.
static Real	valueOf(double doubleValue)	Returns the real number (inexact except for 0.0) corresponding to the specified double value.
static Real	valueOf(long longValue)	Returns the exact real number corresponding to the specified long value (convenience method).
static Real	valueOf(CharSequence chars)	Returns the real for the specified character sequence.
static Real	valueOf(LargeInteger significand, int error, int exponent)	Returns a real having the specified significand, error and exponent values.

Methods inherited from class org.jscience.mathematics.number.Number

byteValue, floatValue, intValue, isGreaterThan, isLessThan, pow, shortValue, toString

Methods inherited from class java.lang.Object

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

Field Details

NaN

public static final Real NaN

Holds a Not-a-Number instance (infinite error).

ZERO

public static final Real ZERO

Holds the exact ZERO instance.

ONE

public static final Real ONE

Holds the exact ONE instance.

Method Details

getExactPrecision

public static int getExactPrecision()

Returns the local minimum precision (number of exact digits) when exact numbers have to be approximated.

Returns:

the minimum number of digits assumed exact for exact real numbers.

setExactPrecision

public static void setExactPrecision(int precision)

Sets the local minimum precision (number of exact digits) when exact numbers have to be approximated.

Parameters:

precision - the minimum number of digits assumed exact for exact numbers.

valueOf

public static Real valueOf(LargeInteger significand,
 int error,
 int exponent)

Returns a real having the specified significand, error and exponent values. If the error is 0, the real is assumed exact. For example:[code] // x = 0.0 ± 0.01 Real x = Real.valueOf(LargeInteger.ZERO, 1, -2); // y = -12.3 exact Real y = Real.valueOf(LargeInteger.valueOf(-123), 0, -1); [/code]

Parameters:

significand - this real significand.

error - the maximum error on the significand.

exponent - the decimal exponent.

Returns:

(significand ± error)·10exponent)

Throws:

IllegalArgumentException - if error < 0

valueOf

public static Real valueOf(double doubleValue)

Returns the real number (inexact except for 0.0) corresponding to the specified double value. The error is derived from the inexact representation of double values intrinsic to the 64 bits IEEE 754 format.

Parameters:

doubleValue - the double value to convert.

Returns:

the corresponding real number.

valueOf

public static Real valueOf(long longValue)

Returns the exact real number corresponding to the specified long value (convenience method).

Parameters:

longValue - the exact long value.

Returns:

Real.valueOf(LargeInteger.valueOf(longValue), 0, 0)

valueOf

public static Real valueOf(CharSequence chars)
                    throws NumberFormatException

Returns the real for the specified character sequence. If the precision is not specified (using the ± symbol), the real is supposed exact. Example of valid character sequences:

"1.2E3" (1200 exact)

"1.2E3±1E-2" (1200 ± 0.01)