geos Namespace Reference

Basic namespace for all GEOS functionalities. More...

Namespaces
	algorithm
	Contains classes and interfaces implementing fundamental computational geometry algorithms.
	geom
	geomgraph
	Contains classes that implement topology graphs.
	index
	Provides classes for various kinds of spatial indexes.
	io
	Contains the interfaces for converting JTS objects to and from other formats.
	linearref
	Contains classes and interfaces implementing linear referencing on linear geometries.
	noding
	Classes to compute nodings for arrangements of line segments and line segment sequences.
	operation
	Provides classes for implementing operations on geometries.
	planargraph
	Contains classes to implement a planar graph data structure.
	precision
	Provides classes for manipulating the precision model of Geometries.
	simplify
	Classes which implement algorithms for simplifying or generalizing geometries.
	triangulate
	Classes to compute Delaunay triangulations.
	util
	Utility classes for GEOS.

Functions
template<class T >
void	ignore_unused_variable_warning (T const &)

Variables
constexpr double	MATH_PI = 3.14159265358979323846
constexpr double	DoubleNotANumber = std::numeric_limits<double>::quiet_NaN()
constexpr double	DoubleMax = (std::numeric_limits<double>::max)()
constexpr double	DoubleInfinity = (std::numeric_limits<double>::infinity)()
constexpr double	DoubleNegInfinity = (-(std::numeric_limits<double>::infinity)())

Detailed Description

Basic namespace for all GEOS functionalities.

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 architecture) 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.

For example, the following code example constructs three DD instances: two to hold the input values and one to hold the result of the addition.

    DD a = new DD(2.0);
    DD b = new DD(3.0);
    DD c = a.add(b);

In contrast, the following approach uses only one object:

    DD a = new DD(2.0);
    a.selfAdd(3.0);

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