GeoMath (Java implementation of GeographicLib 1.49 API)

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`).
`static double`	`epsilon` Equivalent to C++'s `numeric_limits<double>::epsilon()`.
`static double`	`min` Equivalent to C++'s `numeric_limits<double>::min()`.

Method Summary

All Methods Static Methods Concrete Methods
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 (restricted input range).
`static double`	`AngRound(double x)`
`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`	`cbrt(double x)` The cube root function.
`static double`	`copysign(double x, double y)` Copy the sign.
`static double`	`hypot(double x, double y)` The hypotenuse function avoiding underflow and overflow.
`static boolean`	`isfinite(double x)` Test for finiteness.
`static double`	`LatFix(double x)` Normalize a latitude.
`static double`	`log1p(double x)` log(1 + x) accurate near x = 0.
`static Pair`	`norm(double sinx, double cosx)`
`static double`	`polyval(int N, double[] p, int s, double x)` Evaluate a polynomial.
`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
  - epsilon
```
public static final double epsilon
```
    Equivalent to C++'s numeric_limits<double>::epsilon(). In Java version 1.5 and later, Math.ulp(1.0) can be used.
  - min
```
public static final double min
```
    Equivalent to C++'s numeric_limits<double>::min(). In Java version 1.6 and later, Double.MIN_NORMAL can be used.
- Method Detail
  - sq
```
public static double sq(double x)
```
    Square a number.
    
    Parameters:
    
    x - the argument.
    
    Returns:
    
    x².
  - hypot
```
public static double hypot(double x,
                           double y)
```
    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).
  - log1p
```
public static double log1p(double x)
```
    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).
  - atanh
```
public static double atanh(double x)
```
    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).
  - copysign
```
public static double copysign(double x,
                              double y)
```
    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.
  - cbrt
```
public static double cbrt(double x)
```
    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.
  - norm
```
public static Pair norm(double sinx,
                        double cosx)
```
  - 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)
```
  - AngNormalize
```
public static double AngNormalize(double x)
```
    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.
  - 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.

Class GeoMath

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

digits

epsilon

min

Method Detail

sq

hypot

log1p

atanh

copysign

cbrt

norm

sum

polyval

AngRound

AngNormalize

LatFix

AngDiff

sincosd

atan2d

isfinite