net.sf.geographiclib

Class GeoMath

java.lang.Object

net.sf.geographiclib.GeoMath

public class GeoMath
extends Object

Mathematical functions needed by GeographicLib.

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

Field Summary

Fields

Modifier and Type	Field and Description
static int	digits The number of binary digits in the fraction of a double precision number (equivalent to C++'s numeric_limits<double>::digits).

Method Summary

Modifier and Type	Method and Description
static Pair	AngDiff(double x, double y) The exact difference of two angles reduced to (−180°, 180°].
static double	AngNormalize(double x) Normalize an angle.
static double	AngRound(double x) Coarsen a value close to zero.
static double	atan2d(double y, double x) Evaluate the atan2 function with the result in degrees
static double	atanh(double x) The inverse hyperbolic tangent function.
static boolean	isfinite(double x) Test for finiteness.
static double	LatFix(double x) Normalize a latitude.
static Pair	norm(double sinx, double cosx) Normalize a sine cosine pair.
static double	polyval(int N, double[] p, int s, double x) Evaluate a polynomial.
static double	remainder(double x, double y) The remainder function.
static Pair	sincosd(double x) Evaluate the sine and cosine function with the argument in degrees
static double	sq(double x) Square a number.
static Pair	sum(double u, double v) The error-free sum of two numbers.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

digits

public static final int digits

The number of binary digits in the fraction of a double precision number (equivalent to C++'s numeric_limits<double>::digits).

See Also:

Constant Field Values

Method Detail

sq

public static double sq(double x)

Square a number.

Parameters:

x - the argument.

Returns:

x².

atanh

public static double atanh(double x)

The inverse hyperbolic tangent function. This is defined in terms of Math.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).

norm

public static Pair norm(double sinx,
                        double cosx)

Normalize a sine cosine pair.

Parameters:

sinx - the sine.

cosx - the cosine.

Returns:

a Pair of normalized quantities with sinx² + cosx² = 1.

sum

public static Pair sum(double u,
                       double v)

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.

polyval

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

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.

AngRound

public static double AngRound(double x)

Coarsen a value close to zero.

Parameters:

x - the argument

Returns:

the coarsened value.

This makes the smallest gap in x = 1/16 − nextafter(1/16, 0) = 1/2⁵⁷ for reals = 0.7 pm on the earth if x is an angle in degrees. (This is about 1000 times more resolution than we get with angles around 90 degrees.) We use this to avoid having to deal with near singular cases when x is non-zero but tiny (e.g., 10⁻²⁰⁰). This converts −0 to +0; however tiny negative numbers get converted to −0.

remainder

public static double remainder(double x,
                               double y)

The remainder function.

Parameters:

x - the numerator of the division

y - the denominator of the division

Returns:

the remainder in the range [−y/2, y/2].

The range of x is unrestricted; y must be positive.

AngNormalize

public static double AngNormalize(double x)

Normalize an angle.

Parameters:

x - the angle in degrees.

Returns:

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

The range of x is unrestricted.

LatFix

public static double LatFix(double x)

Normalize a latitude.

Parameters:

x - the angle in degrees.

Returns:

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

AngDiff

public static Pair AngDiff(double x,
                           double y)

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.

sincosd

public static Pair sincosd(double x)

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°.

atan2d

public static double atan2d(double y,
                            double x)

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°.

isfinite

public static boolean isfinite(double x)

Test for finiteness.

Parameters:

x - the argument.

Returns:

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