Static Public Member Functions
static Pair	AngDiff (double x, double y)

static double	AngNormalize (double x)

static double	AngRound (double x)

static double	atan2d (double y, double x)

static double	atanh (double x)

static double	cbrt (double x)

static double	copysign (double x, double y)

static double	hypot (double x, double y)

static boolean	isfinite (double x)

static double	LatFix (double x)

static double	log1p (double x)

static Pair	norm (double sinx, double cosx)

static double	polyval (int N, double p[], int s, double x)

static Pair	sincosd (double x)

static double	sq (double x)

static Pair	sum (double u, double v)

Static Public Attributes
static final int	digits = 53

static final double	epsilon = Math.pow(0.5, digits - 1)

static final double	min = Math.pow(0.5, 1022)

Private Member Functions
	GeoMath ()

Detailed Description

Mathematical functions needed by GeographicLib.

Define mathematical functions and constants so that any version of Java can be used.

Definition at line 16 of file GeoMath.java.

Constructor & Destructor Documentation

net.sf.geographiclib.GeoMath.GeoMath ( )

inlineprivate

Definition at line 308 of file GeoMath.java.

Member Function Documentation

static Pair net.sf.geographiclib.GeoMath.AngDiff	(	double	x,
		double	y
	)

inlinestatic

The exact difference of two angles reduced to (−180°, 180°].

Parameters

x	the first angle in degrees.
y	the second angle in degrees.

Returns: Pair(d, e) with d being the rounded difference and e being the error.

The computes z = y − x exactly, reduced to (−180°, 180°]; and then sets z = d + e where d is the nearest representable number to z and e is the truncation error. If d = −180, then e > 0; If d = 180, then e ≤ 0.

Definition at line 221 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.AngNormalize ( double x )

inlinestatic

Normalize an angle (restricted input range).

Parameters

x	the angle in degrees.

Returns: the angle reduced to the range [−180°, 180°).

The range of x is unrestricted.

Definition at line 191 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.AngRound ( double x )

inlinestatic

Definition at line 168 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.atan2d	(	double	y,
		double	x
	)

inlinestatic

Evaluate the atan2 function with the result in degrees

Parameters

y	the sine of the angle
x	the cosine of the angle

Returns: atan2(y, x) in degrees.

The result is in the range (−180° 180°]. N.B., atan2d(±0, −1) = +180°; atan2d(−ε, −1) = −180°, for ε positive and tiny; atan2d(±0, 1) = ±0°.

Definition at line 274 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.atanh ( double x )

inlinestatic

The inverse hyperbolic tangent function. This is defined in terms of GeoMath.log1p(x) in order to maintain accuracy near x = 0. In addition, the odd parity of the function is enforced.

Parameters

x	the argument.

Returns: atanh(x).

Definition at line 90 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.cbrt ( double x )

inlinestatic

The cube root function. In Java version 1.5 and later, Math.cbrt can be used.

Parameters

x	the argument.

Returns: the real cube root of x.

Definition at line 115 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.copysign	(	double	x,
		double	y
	)

inlinestatic

Copy the sign. In Java version 1.6 and later, Math.copysign can be used.

Parameters

x	gives the magitude of the result.
y	gives the sign of the result.

Returns: value with the magnitude of x and with the sign of y.

Definition at line 104 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.hypot	(	double	x,
		double	y
	)

inlinestatic

The hypotenuse function avoiding underflow and overflow. In Java version 1.5 and later, Math.hypot can be used.

Parameters

x	the first argument.
y	the second argument.

Returns: sqrt(x² + y²).

Definition at line 49 of file GeoMath.java.

static boolean net.sf.geographiclib.GeoMath.isfinite ( double x )

inlinestatic

Test for finiteness.

Parameters

x	the argument.

Returns: true if number is finite, false if NaN or infinite.

Definition at line 304 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.LatFix ( double x )

inlinestatic

Normalize a latitude.

Parameters

x	the angle in degrees.

Returns: x if it is in the range [−90°, 90°], otherwise return NaN.

Definition at line 203 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.log1p ( double x )

inlinestatic

log(1 + x) accurate near x = 0. In Java version 1.5 and later, Math.log1p can be used.

This is taken from D. Goldberg, What every computer scientist should know about floating-point arithmetic (1991), Theorem 4. See also, N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd Edition (SIAM, 2002), Answer to Problem 1.5, p 528.

Parameters

x	the argument.

Returns: log(1 + x).

Definition at line 71 of file GeoMath.java.

static Pair net.sf.geographiclib.GeoMath.norm	(	double	sinx,
		double	cosx
	)

inlinestatic

Definition at line 120 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.polyval	(	int	N,
		double	p[],
		int	s,
		double	x
	)

inlinestatic

Evaluate a polynomial.

Parameters

N	the order of the polynomial.
p	the coefficient array (of size N + s + 1 or more).
s	starting index for the array.
x	the variable.

Returns: the value of the polynomial.

Evaluate y = ∑_n=0..N p_s+n x^N−n. Return 0 if N < 0. Return p_s, if N = 0 (even if x is infinite or a nan). The evaluation uses Horner's method.

Definition at line 162 of file GeoMath.java.

static Pair net.sf.geographiclib.GeoMath.sincosd ( double x )

inlinestatic

Evaluate the sine and cosine function with the argument in degrees

Parameters

x	in degrees.

Returns: Pair(s, t) with s = sin(x) and c = cos(x).

The results obey exactly the elementary properties of the trigonometric functions, e.g., sin 9° = cos 81° = − sin 123456789°.

Definition at line 240 of file GeoMath.java.

static double net.sf.geographiclib.GeoMath.sq ( double x )

inlinestatic

Square a number.

Parameters

x	the argument.

Returns: x².

Definition at line 39 of file GeoMath.java.

static Pair net.sf.geographiclib.GeoMath.sum	(	double	u,
		double	v
	)

inlinestatic

The error-free sum of two numbers.

Parameters

u	the first number in the sum.
v	the second number in the sum.

Returns: Pair(s, t) with s = round(u + v) and t = u + v - s.

See D. E. Knuth, TAOCP, Vol 2, 4.2.2, Theorem B.

Definition at line 135 of file GeoMath.java.

Member Data Documentation

final int net.sf.geographiclib.GeoMath.digits = 53

static

The number of binary digits in the fraction of a double precision number (equivalent to C++'s

numeric_limits<double>::digits

).

Definition at line 21 of file GeoMath.java.

final double net.sf.geographiclib.GeoMath.epsilon = Math.pow(0.5, digits - 1)

static

Equivalent to C++'s

numeric_limits<double>::epsilon()

. In Java version 1.5 and later, Math.ulp(1.0) can be used.

Definition at line 26 of file GeoMath.java.

final double net.sf.geographiclib.GeoMath.min = Math.pow(0.5, 1022)

static

Equivalent to C++'s

numeric_limits<double>::min()

. In Java version 1.6 and later, Double.MIN_NORMAL can be used.

Definition at line 31 of file GeoMath.java.

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

GeoMath.java

Static Public Member Functions

Static Public Attributes

Private Member Functions

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation