JScience v4.3

org.jscience.mathematics.number
Class Real

java.lang.Object
  extended by java.lang.Number
      extended by org.jscience.mathematics.number.Number<Real>
          extended by org.jscience.mathematics.number.Real
All Implemented Interfaces:
java.io.Serializable, java.lang.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.

Version:
3.3, January 8, 2006
Author:
Jean-Marie Dautelle
See Also:
Wikipedia: Real number, Serialized Form

Field Summary
static Real NaN
          Holds a Not-a-Number instance (infinite error).
static Real ONE
          Holds the exact ONE instance.
static Real ZERO
          Holds the exact ZERO instance.
 
Method Summary
 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(java.lang.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.
 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(java.lang.CharSequence chars)
          Returns the real for the specified character sequence.
static Real valueOf(double doubleValue)
          Returns the real number (inexact except for 0.0) corresponding to the specified double value.
static Real valueOf(LargeInteger significand, int error, int exponent)
          Returns a real having the specified significand, error and exponent values.
static Real valueOf(long longValue)
          Returns the exact real number corresponding to the specified long value (convenience method).
 
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 Detail

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 Detail

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:
 
     // 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);
 
 

Parameters:
significand - this real significand.
error - the maximum error on the significand.
exponent - the decimal exponent.
Returns:
(significand ± error)·10exponent)
Throws:
java.lang.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(java.lang.CharSequence chars)
                    throws java.lang.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)
  • Parameters:
    chars - the character sequence.
    Returns:
    the corresponding real number.
    Throws:
    java.lang.NumberFormatException - if the character sequence does not contain a parsable real.

    getSignificand

    public LargeInteger getSignificand()
    Returns this real significand value.

    Returns:
    the significand.

    getError

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

    Returns:
    the maximum error on the significand.

    getExponent

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

    Returns:
    the decimal exponent.

    isExact

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

    Returns:
    getError() == 0

    getAccuracy

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

    Returns:
    a measure of the absolute error of this real number.

    getPrecision

    public final int getPrecision()
    Returns the total number of decimal digits guaranteed exact (relative error).

    Returns:
    a measure of the relative error of this real number.

    isPositive

    public boolean isPositive()
    Indicates if this real is greater than zero.

    Returns:
    this > 0

    isNegative

    public boolean isNegative()
    Indicates if this real is less than zero.

    Returns:
    this < 0

    isNaN

    public boolean isNaN()
    Indicates if this real is Not-a-Number (unbounded value interval).

    Returns:
    true if this number has unbounded value interval; false otherwise.

    approximates

    public boolean approximates(Real that)
    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 isNaN() (basically Not-A-Number approximates anything).

    Parameters:
    that - the real to compare with.
    Returns:
    this ≈ that

    round

    public LargeInteger round()
    Returns the closest integer value to this rational number.

    Returns:
    this real rounded to the nearest integer.
    Throws:
    java.lang.ArithmeticException - if this.isNaN()

    opposite

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

    Specified by:
    opposite in interface GroupAdditive<Real>
    Returns:
    -this.

    plus

    public Real plus(Real that)
    Returns the sum of this real number with the one specified.

    Specified by:
    plus in interface GroupAdditive<Real>
    Parameters:
    that - the real to be added.
    Returns:
    this + that.

    minus

    public Real minus(Real that)
    Returns the difference between this real number and the one specified.

    Overrides:
    minus in class Number<Real>
    Parameters:
    that - the real to be subtracted.
    Returns:
    this - that.

    times

    public Real times(long multiplier)
    Returns the product of this real number with the specified long multiplier.

    Parameters:
    multiplier - the long multiplier.
    Returns:
    this · multiplier.

    times

    public Real times(Real that)
    Returns the product of this real number with the one specified.

    Specified by:
    times in interface GroupMultiplicative<Real>
    Specified by:
    times in interface Ring<Real>
    Parameters:
    that - the real multiplier.
    Returns:
    this · that.

    divide

    public Real divide(long divisor)
    Returns this real number divided by the specified int divisor.

    Parameters:
    divisor - the int divisor.
    Returns:
    this / divisor

    divide

    public Real divide(Real that)
    Returns this real number divided by the one specified.

    Parameters:
    that - the real divisor.
    Returns:
    this / that.
    Throws:
    java.lang.ArithmeticException - if that.equals(ZERO)

    inverse

    public Real inverse()
    Returns the reciprocal (or inverse) of this real number.

    Specified by:
    inverse in interface GroupMultiplicative<Real>
    Returns:
    1 / this.

    abs

    public Real abs()
    Returns the absolute value of this real number.

    Returns:
    |this|.

    isLargerThan

    public boolean isLargerThan(Real that)
    Compares the absolute value of two real numbers.

    Specified by:
    isLargerThan in class Number<Real>
    Parameters:
    that - the real number to be compared with.
    Returns:
    |this| > |that|

    sqrt

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

    Returns:
    the positive square root of this real number.

    toText

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

    Specified by:
    toText in interface javolution.lang.Realtime
    Specified by:
    toText in class Number<Real>
    Returns:
    the text representation of this number.

    equals

    public boolean equals(java.lang.Object that)
    Compares this real number against the specified object.

    Note: This method returns true if this or that is Not-A-Number, even though Double.NaN == Double.NaN has the value false.

    Specified by:
    equals in class Number<Real>
    Parameters:
    that - the object to compare with.
    Returns:
    true if the objects are two reals with same significand, error and exponent;false otherwise.

    hashCode

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

    Specified by:
    hashCode in class Number<Real>
    Returns:
    the hash code value.

    longValue

    public long longValue()
    Returns the value of this real number as a long.

    Specified by:
    longValue in class Number<Real>
    Returns:
    the numeric value represented by this real after conversion to type long.

    doubleValue

    public double doubleValue()
    Returns the value of this real number as a double.

    Specified by:
    doubleValue in class Number<Real>
    Returns:
    the numeric value represented by this real after conversion to type double.

    compareTo

    public int compareTo(Real that)
    Compares two real numbers numerically.

    Specified by:
    compareTo in interface java.lang.Comparable<Real>
    Specified by:
    compareTo in class Number<Real>
    Parameters:
    that - the real to compare with.
    Returns:
    -1, 0 or 1 as this real is numerically less than, equal to, or greater than that.
    Throws:
    java.lang.ClassCastException - that is not a Real.

    copy

    public Real copy()
    Description copied from class: Number
    Returns a copy of this number allocated by the calling thread (possibly on the stack).

    Specified by:
    copy in interface javolution.lang.ValueType
    Specified by:
    copy in class Number<Real>
    Returns:
    an identical and independant copy of this number.

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