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 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

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static void`	`AngDiff(Pair p, 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 double`	`LatFix(double x)`	Normalize a latitude.
`static void`	`norm(Pair p, double sinx, double cosx)`	Normalize a sine cosine pair.
`static double`	`polyval(int N, double[] p, int s, double x)`	Evaluate a polynomial.
`static void`	`sincosd(Pair p, double x)`	Evaluate the sine and cosine function with the argument in degrees
`static void`	`sincosde(Pair p, double x, double t)`	Evaluate the sine and cosine function with reduced argument plus correction
`static double`	`sq(double x)`	Square a number.
`static void`	`sum(Pair p, 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 void norm(Pair p,
                        double sinx,
                        double cosx)
```
    Normalize a sine cosine pair.
    
    Parameters:
    
    p - return parameter for normalized quantities with sinx² + cosx² = 1.
    
    sinx - the sine.
    
    cosx - the cosine.
  - sum
```
public static void sum(Pair p,
                       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.
    
    p - output 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.
  - 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 void AngDiff(Pair p,
                           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.
    
    p - output Pair(d, e) with d being the rounded difference and e being the error.
    This 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 z = ±0° or ±180°, then the sign of d is given by the sign of y − x. The maximum absolute value of e is 2⁻²⁶ (for doubles).
  - sincosd
```
public static void sincosd(Pair p,
                           double x)
```
    Evaluate the sine and cosine function with the argument in degrees
    
    Parameters:
    
    p - return Pair(s, t) with s = sin(x) and c = cos(x).
    
    x - in degrees.
    The results obey exactly the elementary properties of the trigonometric functions, e.g., sin 9° = cos 81° = − sin 123456789°.
  - sincosde
```
public static void sincosde(Pair p,
                            double x,
                            double t)
```
    Evaluate the sine and cosine function with reduced argument plus correction
    
    Parameters:
    
    p - return Pair(s, t) with s = sin(x + t) and c = cos(x + t).
    
    x - reduced angle in degrees.
    
    t - correction in degrees.
    This is a variant of GeoMath.sincosd allowing a correction to the angle to be supplied. x x must be in [−180°, 180°] and t is assumed to be a small correction. GeoMath.AngRound is applied to the reduced angle to prevent problems with x + t being extremely close but not exactly equal to one of the four cardinal directions.
  - 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°.

Class GeoMath

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

digits

Method Detail

sq

atanh

norm

sum

polyval

AngRound

AngNormalize

LatFix

AngDiff

sincosd

sincosde

atan2d