**'org.jscience.mathematics.number.Real'**Java class

## 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 Realextends 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 \xc2\xb1 error) \xc2\xb7 10`

).^{exponent}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

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