# Package org.jscience.mathematics.number

Provides common types of numbers most of them implementing the

`field`

interface.See: Description

Class Summary Class Description Complex This class represents an immutable complex number.Float64 This class represents a 64 bits floating point number.FloatingPoint This class represents a floating point number of arbitrary precision.Integer64 This class represents a 64 bits integer number.LargeInteger This class represents an immutable integer number of arbitrary size.ModuloInteger This class represents a modulo integer.Number<T extends Number<T>> This class represents a`value-type`

number.Rational This class represents the ratio of two`LargeInteger`

numbers.Real This class represents a real number of arbitrary precision with known/guaranteed uncertainty.

## Package org.jscience.mathematics.number Description

Provides common types of numbers most of them implementing the `field`

interface.

Although numbers defined in this package are not as fast as primitives types (e.g. `int`

or `double`

). They have many advantages (such as arbitrary size for `LargeInteger`

or precision for `Real`

) which make them irreplaceable in some calculations. This can be illustrated with the following example:

double x = 10864; double y = 18817; double z = 9 * Math.pow(x, 4.0)- Math.pow(y, 4.0) + 2 * Math.pow(y, 2.0); System.out.println("Result : " + z); > Result : 2.0The mathematically correct value is z=1. However, Java compilers using ANSI/IEEE double precision numbers evaluate z=2. Not even the first digit is correct! This is due to a rounding error occurring when subtracting two nearly equal floating point numbers. Now, lets write the same formula using

`Real`

numbers:int accuracy = 20; // 20 decimal zeros for integer values. Real x = Real.valueOf(10864, accuracy); Real y = Real.valueOf(18817, accuracy); Real z = x.pow(4).times(9).plus(y.pow(4).opposite()).plus(y.pow(2).times(2)); System.out.println("Result : " + z); > Result : 1.00000Not only the correct result is returned, but this result is also

**guaranteed**to be

`1 \xc2\xb1 0.00001`

. Only exact digits are written out, for example the following displays the first exact digits of `sqrt(2)`

: Real two = Real.valueOf(2, 100); // 2.0000..00 (100 zeros after decimal point). Real sqrt2 = two.sqrt(); System.out.println("sqrt(2) = " + sqrt2); System.out.println("Precision = " + sqrt2.getPrecision() + " digits."); > sqrt(2) = 1.414213562373095048801688724209698078569671875376948 > Precision = 53 digits.

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