Namespace NetTopologySuite.Mathematics

Classes

MathUtil

Various utility functions for mathematical and numerical operations.

Matrix

Implements some 2D matrix operations (in particular, solving systems of linear equations).

Plane3D

Models a plane in 3-dimensional Cartesian space.

Vector2D

A 2-dimensional mathematical vector represented by double-precision X and Y components.

Vector3D

Represents a vector in 3-dimensional Cartesian space.

VectorMath

Functions for performing vector mathematics.

Structs

DD

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.

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

Enums

Plane

Enumeration for the 3 coordinate planes