Implements extended-precision floating-point numbers which maintain 106 bits (approximately 30 decimal digits) of precision. A DoubleDouble uses a representation containing two double-precision values. A number x is represented as a pair of doubles, x.hi and x.lo, such that the number represented by x is x.hi + x.lo, where More...

Inheritance diagram for NetTopologySuite.Mathematics.DD:

Public Member Functions
	DD (double x)
	Creates a new DD with value x. More...

	DD (double hi, double lo)
	Creates a new DD with value (hi, lo). More...

	DD (DD dd)
	Creates a DD with a value equal to the argument More...

	DD (String str)

Object	Clone ()
	Creates and returns a copy of this value. More...

DD	Add (DD y)
	Returns a DD whose value is `(this + y )` More...

DD	Add (double y)
	Returns a DD whose value is `(this + y)`. More...

DD	Subtract (DD y)
	Computes a new DD object whose value is `(this - y)`. More...

DD	Subtract (double y)
	Computes a new DD object whose value is `(this - y)`. More...

DD	Negate ()
	Returns a DD whose value is `-this`. More...

DD	Multiply (DD y)

DD	Multiply (double y)

DD	Divide (DD y)
	Computes a new DD whose value is `(this / y)`. More...

DD	Divide (double y)
	Computes a new DD whose value is `(this / y)`. More...

DD	Reciprocal ()

DD	Min (DD x)
	Computes the minimum of this and another DD number. More...

DD	Max (DD x)
	Computes the maximum of this and another DD number. More...

DD	Floor ()

DD	Ceiling ()

int	Signum ()
	Returns an integer indicating the sign of this value. More...

DD	Rint ()
	Rounds this value to the nearest integer. The value is rounded to an integer by adding 1/2 and taking the floor of the result. Special cases: If this value is NaN, returns NaN. More...

DD	Truncate ()
	Returns the integer which is largest in absolute value and not further from zero than this value. Special cases: If this value is NaN, returns NaN. More...

DD	Abs ()
	Returns the absolute value of this value. Special cases: if this value is NaN, it is returned. More...

DD	Sqr ()
	Computes the square of this value. More...

DD	Sqrt ()

DD	Pow (int exp)
	Computes the value of this number raised to an integral power. Follows semantics of .Net Math.Pow as closely as possible. More...

double	ToDoubleValue ()

int	ToIntValue ()

bool	IsPositive ()
	Gets a value indicating whether this object is positive or not More...

bool	Equals (DD y)

bool	GreaterThan (DD y)

bool	GreaterOrEqualThan (DD y)

bool	LessThan (DD y)
	Tests whether this value is less than another `DoubleDouble` value. More...

bool	LessOrEqualThan (DD y)

int	CompareTo (DD other)

int	CompareTo (Object o)

String	Dump ()
	Dumps the components of this number to a string. More...

override String	ToString ()
	Returns a string representation of this number, in either standard or scientific notation. If the magnitude of the number is in the range [ 10^-3, 10⁸ ] standard notation will be used. Otherwise, scientific notation will be used. More...

String	ToStandardNotation ()
	Returns the string representation of this value in standard notation. More...

String	ToSciNotation ()
	Returns the string representation of this value in scientific notation. More...

override bool	Equals (object obj)

override int	GetHashCode ()

Static Public Member Functions
static DD	ValueOf (String str)
	Converts the string argument to a DoubleDouble number. More...

static	operator DD (String val)

static DD	ValueOf (double x)

static implicit	operator DD (Double val)

static DD	Copy (DD dd)
	Creates a new DD with the value of the argument. More...

static DD	operator+ (DD lhs, DD rhs)
	Returns the sum of lhs and rhs . More...

static DD	operator+ (DD lhs, Double rhs)
	Returns the sum of lhs and rhs . More...

static DD	operator- (DD lhs, DD rhs)
	Returns the difference of lhs and rhs . More...

static DD	operator- (DD lhs, Double rhs)
	Returns the difference of lhs and rhs . More...

static DD	operator* (DD lhs, Double rhs)

static DD	operator* (DD lhs, DD rhs)

static DD	operator/ (DD lhs, Double rhs)

static DD	operator/ (DD lhs, DD rhs)

static DD	Sqr (double x)
	Computes the square of this value. More...

static DD	Sqrt (double x)

static bool	IsNaN (DD value)
	Gets a value indicating whether this object is positive or not More...

static bool	operator== (DD lhs, DD rhs)

static bool	operator!= (DD rhs, DD lhs)

static DD	Parse (String str)
	Converts a string representation of a real number into a DoubleDouble value. The format accepted is similar to the standard Java real number syntax. It is defined by the following regular expression: More...

Static Public Attributes
static readonly DD	PI
	The value nearest to the constant Pi. More...

static readonly DD	TwoPi
	The value nearest to the constant 2 * Pi. More...

static readonly DD	PiHalf
	The value nearest to the constant Pi / 2. More...

static readonly DD	E
	The value nearest to the constant e (the natural logarithm base). More...

static readonly DD	NaN = new DD(Double.NaN, Double.NaN)
	A value representing the result of an operation which does not return a valid number. More...

static readonly double	Epsilon = 1.23259516440783e-32
	The smallest representable relative difference between two DD values More...

Properties
bool	IsZero `[get]`
	Gets a value indicating whether this object is zero (0) or not More...

bool	IsNegative `[get]`
	Gets a value indicating whether this object is negative or not More...

Detailed Description

Implements extended-precision floating-point numbers which maintain 106 bits (approximately 30 decimal digits) of precision.

A DoubleDouble uses a representation containing two double-precision values. A number x is represented as a pair of doubles, x.hi and x.lo, such that the number represented by x is x.hi + x.lo, where

    |x.lo| <= 0.5*ulp(x.hi)

and ulp(y) means "unit in the last place of y". The basic arithmetic operations are implemented using convenient properties of IEEE-754 floating-point arithmetic.

The range of values which can be represented is the same as in IEEE-754. The precision of the representable numbers is twice as great as IEEE-754 double precision.

The correctness of the arithmetic algorithms relies on operations being performed with standard IEEE-754 double precision and rounding. This is the Java standard arithmetic model, but for performance reasons Java implementations are not constrained to using this standard by default. Some processors (notably the Intel Pentium architecure) perform floating point operations in (non-IEEE-754-standard) extended-precision. A JVM implementation may choose to use the non-standard extended-precision as its default arithmetic mode. To prevent this from happening, this code uses the Java strictfp modifier, which forces all operations to take place in the standard IEEE-754 rounding model.

The API provides both a set of value-oriented operations and a set of mutating operations. Value-oriented operations treat DoubleDouble values as immutable; operations on them return new objects carrying the result of the operation. This provides a simple and safe semantics for writing DoubleDouble expressions. However, there is a performance penalty for the object allocations required. The mutable interface updates object values in-place. It provides optimum memory performance, but requires care to ensure that aliasing errors are not created and constant values are not changed.

This implementation uses algorithms originally designed variously by Knuth, Kahan, Dekker, and Linnainmaa. Douglas Priest developed the first C implementation of these techniques. Other more recent C++ implementation are due to Keith M. Briggs and David Bailey et al.

References

Priest, D., Algorithms for Arbitrary Precision Floating Point Arithmetic, in P. Kornerup and D. Matula, Eds., Proc. 10th Symposium on Computer Arithmetic, IEEE Computer Society Press, Los Alamitos, Calif., 1991.
Yozo Hida, Xiaoye S. Li and David H. Bailey, Quad-Double Arithmetic: Algorithms, Implementation, and Application, manuscript, Oct 2000; Lawrence Berkeley National Laboratory Report BNL-46996.
David Bailey, High Precision Software Directory; http://crd.lbl.gov/~dhbailey/mpdist/index.html

<author>Martin Davis</author>

Constructor & Destructor Documentation

NetTopologySuite.Mathematics.DD.DD ( double x )

Creates a new DD with value x.

Parameters

x	The initial value

NetTopologySuite.Mathematics.DD.DD	(	double	hi,
		double	lo
	)

Creates a new DD with value (hi, lo).

Parameters

hi	The high order component
lo	The low order component

NetTopologySuite.Mathematics.DD.DD ( DD dd )

Creates a DD with a value equal to the argument

Parameters

dd	The initial value

NetTopologySuite.Mathematics.DD.DD ( String str )

Creates a new DoubleDouble with value equal to the argument.

Parameters

str	the value to initialize by

Exceptions

NumberFormatException if str is not a valid representation of a number

Member Function Documentation

DD NetTopologySuite.Mathematics.DD.Abs ( )

Returns the absolute value of this value. Special cases:

if this value is NaN, it is returned.

Returns: The absolute value of this value

DD NetTopologySuite.Mathematics.DD.Add ( DD y )

Returns a DD whose value is (this + y )

Parameters

y	The addende

"/> <returns><c>(this + <paramref name="y"/>)

DD NetTopologySuite.Mathematics.DD.Add ( double y )

Returns a DD whose value is (this + y).

Parameters

y	The addend

Returns: (this + y)

DD NetTopologySuite.Mathematics.DD.Ceiling ( )

Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer. Special cases:

If this value is NaN, returns NaN.

Returns: the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer.

Object NetTopologySuite.Mathematics.DD.Clone ( )

Creates and returns a copy of this value.

Returns: Acopy of this value

int NetTopologySuite.Mathematics.DD.CompareTo ( DD other )

Compares two DoubleDouble objects numerically.

Returns: -1,0 or 1 depending on whether this value is less than, equal to or greater than the value of o

static DD NetTopologySuite.Mathematics.DD.Copy ( DD dd )

static

Creates a new DD with the value of the argument.

Parameters

dd	The value to copy

Returns: A copy of dd

DD NetTopologySuite.Mathematics.DD.Divide ( DD y )

Computes a new DD whose value is (this / y).

Parameters

y	The divisor

Returns: A new DD with the value (this / y)

DD NetTopologySuite.Mathematics.DD.Divide ( double y )

Computes a new DD whose value is (this / y).

Parameters

y	The divisor

Returns: A new DD with the value (this / y)

String NetTopologySuite.Mathematics.DD.Dump ( )

Dumps the components of this number to a string.

Returns: A string showing the components of the number

bool NetTopologySuite.Mathematics.DD.Equals ( DD y )

Tests whether this value is equal to another DoubleDouble value.

Parameters

y	a DoubleDouble value

Returns: true if this value = y

DD NetTopologySuite.Mathematics.DD.Floor ( )

Returns the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer. Special cases:

If this value is NaN, returns NaN.

Returns: the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer.

bool NetTopologySuite.Mathematics.DD.GreaterOrEqualThan ( DD y )

Tests whether this value is greater than or equals to another DoubleDouble value.

Parameters

y	a DoubleDouble value

Returns: true if this value >= y

bool NetTopologySuite.Mathematics.DD.GreaterThan ( DD y )

Tests whether this value is greater than another DoubleDouble value.

Parameters

y	a DoubleDouble value

Returns: true if this value > y

static bool NetTopologySuite.Mathematics.DD.IsNaN ( DD value )

static

Gets a value indicating whether this object is positive or not

bool NetTopologySuite.Mathematics.DD.IsPositive ( )

Gets a value indicating whether this object is positive or not

bool NetTopologySuite.Mathematics.DD.LessOrEqualThan ( DD y )

Tests whether this value is less than or equal to another DoubleDouble value.

Parameters

y	a DoubleDouble value

Returns: true if this value <= y

bool NetTopologySuite.Mathematics.DD.LessThan ( DD y )

Tests whether this value is less than another DoubleDouble value.

Parameters

y	A DoubleDouble value

Returns: true if this value is < y

DD NetTopologySuite.Mathematics.DD.Max ( DD x )

Computes the maximum of this and another DD number.

Parameters

x	A DD number

Returns: The maximum of the two numbers

DD NetTopologySuite.Mathematics.DD.Min ( DD x )

Computes the minimum of this and another DD number.

Parameters

x	A DD number

Returns: The minimum of the two numbers

DD NetTopologySuite.Mathematics.DD.Multiply ( DD y )

Returns a new DoubleDouble whose value is (this * y).

Parameters

y	the multiplicand

Returns: (this * y)

DD NetTopologySuite.Mathematics.DD.Multiply ( double y )

Returns a new DoubleDouble whose value is (this * y).

Parameters

y	the multiplicand

Returns: (this * y)

DD NetTopologySuite.Mathematics.DD.Negate ( )

Returns a DD whose value is -this.

Subtracts the argument from the value of this. To prevent altering constants, this method must only be used on values known to be newly created.

Parameters

y	the addend

Returns: this object, decreased by y Subtracts the argument from the value of this. To prevent altering constants, this method must only be used on values known to be newly created.

Parameters

y	the addend

Returns

this object, decreased by y

Returns: -this

static DD NetTopologySuite.Mathematics.DD.operator*	(	DD	lhs,
		Double	rhs
	)

static

Multiplies this object by the argument, returning this. To prevent altering constants, this method must only be used on values known to be newly created.

Parameters

y	the value to multiply by

Returns: this object, multiplied by y Multiplies this object by the argument, returning this. To prevent altering constants, this method must only be used on values known to be newly created.

Parameters

y	the value to multiply by

Returns: this object, multiplied by y

static DD NetTopologySuite.Mathematics.DD.operator+	(	DD	lhs,
		DD	rhs
	)

static

Returns the sum of lhs and rhs .

Parameters

lhs	The left hand side
rhs	The right hand side

Returns: The sum of lhs and rhs

static DD NetTopologySuite.Mathematics.DD.operator+	(	DD	lhs,
		Double	rhs
	)

static

Returns the sum of lhs and rhs .

Parameters

lhs	The left hand side
rhs	The right hand side

Returns: The sum of lhs and rhs

static DD NetTopologySuite.Mathematics.DD.operator-	(	DD	lhs,
		DD	rhs
	)

static

Returns the difference of lhs and rhs .

Parameters

lhs	The left hand side
rhs	The right hand side

Returns: The difference of lhs and rhs

static DD NetTopologySuite.Mathematics.DD.operator-	(	DD	lhs,
		Double	rhs
	)

static

Returns the difference of lhs and rhs .

Parameters

lhs	The left hand side
rhs	The right hand side

Returns: The difference of lhs and rhs

static DD NetTopologySuite.Mathematics.DD.operator/	(	DD	lhs,
		Double	rhs
	)

static

Divides this object by the argument, returning this. To prevent altering constants, this method must only be used on values known to be newly created.

Parameters

y	the value to divide by

Returns: this object, divided by y

static DD NetTopologySuite.Mathematics.DD.Parse ( String str )

static

Converts a string representation of a real number into a DoubleDouble value. The format accepted is similar to the standard Java real number syntax. It is defined by the following regular expression:

[+|-] {digit} [ . {digit} ] [ ( e | E ) [+|-] {digit}+

Parameters

str	The string to parse

Returns: The value of the parsed number

Exceptions

FormatException Thrown if str is not a valid representation of a number

DD NetTopologySuite.Mathematics.DD.Pow ( int exp )

Computes the value of this number raised to an integral power. Follows semantics of .Net Math.Pow as closely as possible.

Parameters

exp	The integer exponent

Returns: x raised to the integral power exp

DD NetTopologySuite.Mathematics.DD.Reciprocal ( )

Returns a DoubleDouble whose value is 1 / this.

Returns: the reciprocal of this value

DD NetTopologySuite.Mathematics.DD.Rint ( )

Rounds this value to the nearest integer. The value is rounded to an integer by adding 1/2 and taking the floor of the result. Special cases:

If this value is NaN, returns NaN.

Returns: This value rounded to the nearest integer

int NetTopologySuite.Mathematics.DD.Signum ( )

Returns an integer indicating the sign of this value.

if this value is > 0, returns 1
if this value is < 0, returns -1
if this value is = 0, returns 0
if this value is NaN, returns 0

Returns: An integer indicating the sign of this value

DD NetTopologySuite.Mathematics.DD.Sqr ( )

Computes the square of this value.

Returns: The square of this value

static DD NetTopologySuite.Mathematics.DD.Sqr ( double x )

static

Computes the square of this value.

Returns: The square of this value.

DD NetTopologySuite.Mathematics.DD.Sqrt ( )

Computes the positive square root of this value. If the number is NaN or negative, NaN is returned.

Returns: the positive square root of this number. If the argument is NaN or less than zero, the result is NaN.

DD NetTopologySuite.Mathematics.DD.Subtract ( DD y )

Computes a new DD object whose value is (this - y).

Parameters

y	The subtrahend

Returns: (this - y)

DD NetTopologySuite.Mathematics.DD.Subtract ( double y )

Computes a new DD object whose value is (this - y).

Parameters

y	The subtrahend

Returns: (this - y)

double NetTopologySuite.Mathematics.DD.ToDoubleValue ( )

Converts this value to the nearest double-precision number.

Returns: the nearest double-precision number to this value

int NetTopologySuite.Mathematics.DD.ToIntValue ( )

Converts this value to the nearest integer.

Returns: the nearest integer to this value

String NetTopologySuite.Mathematics.DD.ToSciNotation ( )

Returns the string representation of this value in scientific notation.

Returns: The string representation in scientific notation

String NetTopologySuite.Mathematics.DD.ToStandardNotation ( )

Returns the string representation of this value in standard notation.

Returns: The string representation in standard notation

override String NetTopologySuite.Mathematics.DD.ToString ( )

Returns a string representation of this number, in either standard or scientific notation. If the magnitude of the number is in the range [ 10^-3, 10⁸ ] standard notation will be used. Otherwise, scientific notation will be used.

Returns: A string representation of this number

DD NetTopologySuite.Mathematics.DD.Truncate ( )

Returns the integer which is largest in absolute value and not further from zero than this value. Special cases:

If this value is NaN, returns NaN.

Returns: The integer which is largest in absolute value and not further from zero than this value

static DD NetTopologySuite.Mathematics.DD.ValueOf ( String str )

static

Converts the string argument to a DoubleDouble number.

Parameters

str	A string containing a representation of a numeric value

Returns: The extended precision version of the value

Exceptions

FormatException Thrown if str is not a valid representation of a number

static DD NetTopologySuite.Mathematics.DD.ValueOf ( double x )

static

Converts the double argument to a DoubleDouble number.

Parameters

x	a numeric value

Returns: the extended precision version of the value

Member Data Documentation

readonly DD NetTopologySuite.Mathematics.DD.E

static

Initial value:

= new DD(
            2.718281828459045091e+00,
            1.445646891729250158e-16)

The value nearest to the constant e (the natural logarithm base).

readonly double NetTopologySuite.Mathematics.DD.Epsilon = 1.23259516440783e-32

static

The smallest representable relative difference between two DD values

readonly DD NetTopologySuite.Mathematics.DD.NaN = new DD(Double.NaN, Double.NaN)

static

A value representing the result of an operation which does not return a valid number.

readonly DD NetTopologySuite.Mathematics.DD.PI

static

Initial value:

= new DD(
            3.141592653589793116e+00,
            1.224646799147353207e-16)

The value nearest to the constant Pi.

readonly DD NetTopologySuite.Mathematics.DD.PiHalf

static

Initial value:

= new DD(
            1.570796326794896558e+00,
            6.123233995736766036e-17)

The value nearest to the constant Pi / 2.

readonly DD NetTopologySuite.Mathematics.DD.TwoPi

static

Initial value:

= new DD(
            6.283185307179586232e+00,
            2.449293598294706414e-16)

The value nearest to the constant 2 * Pi.

Property Documentation

bool NetTopologySuite.Mathematics.DD.IsNegative

get

Gets a value indicating whether this object is negative or not

bool NetTopologySuite.Mathematics.DD.IsZero

get

Gets a value indicating whether this object is zero (0) or not

The documentation for this struct was generated from the following file:

NetTopologySuite/NetTopologySuite/Mathematics/DD.cs

Public Member Functions

Static Public Member Functions

Static Public Attributes

Properties

Detailed Description

References

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

Property Documentation