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Java Source Code / Java Documentation » Science » jscience 4.3.1 » org.jscience.mathematics.number

Source Cross Reference Class Diagram Java Document (Java Doc)

org.jscience.mathematics.number .Real

Real

final public class Real extends Number implements Field<Real>(Code)

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

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

The actual Real.getPrecision precision and Real.getAccuracy 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 org.jscience.mathematics.vector.Matrix 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.

author:
   Jean-Marie Dautelle
version:
   3.3, January 8, 2006
See Also:    * Wikipedia: Real number

Field Summary
final public static Real	NaN Holds a Not-a-Number instance (infinite error).
final public static Real	ONE Holds the exact ONE instance.
final static XMLFormat<Real>	XML Holds the default XML representation for real numbers.
final public static Real	ZERO Holds the exact ZERO instance.

Method Summary
public Real	abs() Returns the absolute value of this real number.
public boolean	approximates(Real that) Indicates if this real approximates the one specified.
public int	compareTo(Real that) Compares two real numbers numerically. Parameters: that - the real to compare with.
public Real	copy()
public Real	divide(long divisor) Returns this real number divided by the specified `int` divisor.
public Real	divide(Real that) Returns this real number divided by the one specified. Parameters: that - the real divisor.
public double	doubleValue() Returns the value of this real number as a `double`.
public boolean	equals(Object that) Compares this real number against the specified object. Note: This method returns `true` if `this` or `that` Real.isNaN is Not-A-Number , even though `Double.NaN == Double.NaN` has the value `false`. Parameters: that - the object to compare with.
public int	getAccuracy() Returns the number of decimal digits guaranteed exact which appear to the right of the decimal point (absolute error).
public int	getError() Returns the maximum error (positive) on this real significand.
public static int	getExactPrecision() Returns the javolution.context.LocalContext local minimum precision (number of exact digits) when exact numbers have to be approximated.
public int	getExponent() Returns the exponent of the power of 10 multiplier.
final public int	getPrecision() Returns the total number of decimal digits guaranteed exact (relative error).
public LargeInteger	getSignificand() Returns this real significand value.
public int	hashCode() Returns the hash code for this real number.
public Real	inverse() Returns the reciprocal (or inverse) of this real number.
public boolean	isExact() Indicates if this real number is exact (`Real.getError() error == 0`).
public boolean	isLargerThan(Real that) Compares the absolute value of two real numbers. Parameters: that - the real number to be compared with.
public boolean	isNaN() Indicates if this real is Not-a-Number (unbounded value interval).
public boolean	isNegative() Indicates if this real is less than zero.
public boolean	isPositive() Indicates if this real is greater than zero.
public long	longValue() Returns the value of this real number as a `long`.
public Real	minus(Real that) Returns the difference between this real number and the one specified. Parameters: that - the real to be subtracted.
public Real	opposite() Returns the negation of this real number.
public Real	plus(Real that) Returns the sum of this real number with the one specified. Parameters: that - the real to be added.
public LargeInteger	round() Returns the closest integer value to this rational number.
public static void	setExactPrecision(int precision) Sets the javolution.context.LocalContext local minimum precision (number of exact digits) when exact numbers have to be approximated.
public Real	sqrt() Returns the square root of this real number, the more accurate is this real number, the more accurate the square root.
public Real	times(long multiplier) Returns the product of this real number with the specified `long` multiplier. Parameters: multiplier - the `long` multiplier.
public Real	times(Real that) Returns the product of this real number with the one specified. Parameters: that - the real multiplier.
public Text	toText() Returns the decimal text representation of this number.
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.
public static Real	valueOf(double doubleValue) Returns the real number (inexact except for `0.0`) corresponding to the specified `double` value.
public static Real	valueOf(long longValue) Returns the exact real number corresponding to the specified `long` value (convenience method).
public static Real	valueOf(CharSequence chars) Returns the real for the specified character sequence. If the precision is not specified (using the `±` symbol), the real is supposed exact.

Field Detail

NaN
final public static Real NaN(Code)
	Holds a Not-a-Number instance (infinite error).

ONE
final public static Real ONE(Code)
	Holds the exact ONE instance.

XML
final static XMLFormat<Real> XML(Code)
	Holds the default XML representation for real numbers. This representation consists of a simple `value` attribute holding the Real.toText() textual representation.

ZERO
final public static Real ZERO(Code)
	Holds the exact ZERO instance.

Method Detail

abs
public Real abs()(Code)
	Returns the absolute value of this real number. `\|this\|`.

approximates
public boolean approximates(Real that)(Code)
	Indicates if this real approximates the one specified. This method takes into account possible errors (e.g. numeric errors) to make this determination. Note: This method returns `true` if `this` or `that` Real.isNaN (basically Not-A-Number approximates anything). Parameters: that - the real to compare with. `this ≈ that`

compareTo
public int compareTo(Real that)(Code)
	Compares two real numbers numerically. Parameters: that - the real to compare with. -1, 0 or 1 as this real is numerically less than, equal to,or greater than `that`. throws: ClassCastException - `that` is not a Real.

copy
public Real copy()(Code)

divide
public Real divide(long divisor)(Code)
	Returns this real number divided by the specified `int` divisor. Parameters: divisor - the `int` divisor. `this / divisor`

divide
public Real divide(Real that)(Code)
	Returns this real number divided by the one specified. Parameters: that - the real divisor. `this / that`. throws: ArithmeticException - if `that.equals(ZERO)`

doubleValue
public double doubleValue()(Code)
	Returns the value of this real number as a `double`. the numeric value represented by this real after conversionto type `double`.

equals
public boolean equals(Object that)(Code)
	Compares this real number against the specified object. Note: This method returns `true` if `this` or `that` Real.isNaN is Not-A-Number , even though `Double.NaN == Double.NaN` has the value `false`. Parameters: that - the object to compare with. `true` if the objects are two reals with same significand, error and exponent;`false` otherwise.

getAccuracy
public int getAccuracy()(Code)
	Returns the number of decimal digits guaranteed exact which appear to the right of the decimal point (absolute error). a measure of the absolute error of this real number.

getError
public int getError()(Code)
	Returns the maximum error (positive) on this real significand. the maximum error on the significand.

getExactPrecision
public static int getExactPrecision()(Code)
	Returns the javolution.context.LocalContext local minimum precision (number of exact digits) when exact numbers have to be approximated. the minimum number of digits assumed exact for Real.isExact exact real numbers.

getExponent
public int getExponent()(Code)
	Returns the exponent of the power of 10 multiplier. the decimal exponent.

getPrecision
final public int getPrecision()(Code)
	Returns the total number of decimal digits guaranteed exact (relative error). a measure of the relative error of this real number.

getSignificand
public LargeInteger getSignificand()(Code)
	Returns this real significand value. the significand.

hashCode
public int hashCode()(Code)
	Returns the hash code for this real number. the hash code value.

inverse
public Real inverse()(Code)
	Returns the reciprocal (or inverse) of this real number. `1 / this`.

isExact
public boolean isExact()(Code)
	Indicates if this real number is exact (`Real.getError() error == 0`). `getError() == 0`

isLargerThan
public boolean isLargerThan(Real that)(Code)
	Compares the absolute value of two real numbers. Parameters: that - the real number to be compared with. `\|this\| > \|that\|`

isNaN
public boolean isNaN()(Code)
	Indicates if this real is Not-a-Number (unbounded value interval). `true` if this number has unbounded value interval;`false` otherwise.

isNegative
public boolean isNegative()(Code)
	Indicates if this real is less than zero. `this < 0`

isPositive
public boolean isPositive()(Code)
	Indicates if this real is greater than zero. `this > 0`

longValue
public long longValue()(Code)
	Returns the value of this real number as a `long`. the numeric value represented by this real after conversionto type `long`.

minus
public Real minus(Real that)(Code)
	Returns the difference between this real number and the one specified. Parameters: that - the real to be subtracted. `this - that`.

opposite
public Real opposite()(Code)
	Returns the negation of this real number. `-this`.

plus
public Real plus(Real that)(Code)
	Returns the sum of this real number with the one specified. Parameters: that - the real to be added. `this + that`.

round
public LargeInteger round()(Code)
	Returns the closest integer value to this rational number. this real rounded to the nearest integer. throws: ArithmeticException - if `this.isNaN()`

setExactPrecision
public static void setExactPrecision(int precision)(Code)
	Sets the javolution.context.LocalContext local minimum precision (number of exact digits) when exact numbers have to be approximated. Parameters: precision - the minimum number of digits assumed exact for Real.isExact exact numbers.

sqrt
public Real sqrt()(Code)
	Returns the square root of this real number, the more accurate is this real number, the more accurate the square root. the positive square root of this real number.

times
public Real times(long multiplier)(Code)
	Returns the product of this real number with the specified `long` multiplier. Parameters: multiplier - the `long` multiplier. `this · multiplier`.

times
public Real times(Real that)(Code)
	Returns the product of this real number with the one specified. Parameters: that - the real multiplier. `this · that`.

toText
public Text toText()(Code)
	Returns the decimal text representation of this number. the text representation of this number.

valueOf
public static Real valueOf(LargeInteger significand, int error, int exponent)(Code)
	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. Parameters: error - the maximum error on the significand. Parameters: exponent - the decimal exponent. `(significand ± error)·10^exponent)` throws: IllegalArgumentException - if `error < 0`

valueOf
public static Real valueOf(double doubleValue)(Code)
	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. the corresponding real number.

valueOf
public static Real valueOf(long longValue)(Code)
	Returns the exact real number corresponding to the specified `long` value (convenience method). Parameters: longValue - the exact long value. `Real.valueOf(LargeInteger.valueOf(longValue), 0, 0)`

valueOf
public static Real valueOf(CharSequence chars) throws NumberFormatException(Code)
	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) Parameters: chars - the character sequence. the corresponding real number. throws: NumberFormatException - if the character sequence does not containa parsable real.

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