Math

java.lang.Object
- cds.healpix.common.math.Math

```
public final class Math
extends java.lang.Object
```
Utility class to easily switch between java.lang.Math and another Math librarie like FastMath, and to define new functions like sinc (sinus cardinal = sin(x) / x). Replace java..lang.Math by org..apache.commons.math3.util.FastMath (using e.g. sed or replaceAll) to use FastMath instead of Math (and vice-versa).

Author:

F.-X. Pineau

Field Summary

Fields
Modifier and Type	Field and Description
`static double`	`EPSILON`
`static double`	`FOUR_OVER_PI`
`static double`	`HALF_PI`
`static double`	`LOG2`
`static double`	`ONE_FOURTH`
`static double`	`ONE_OVER_2PI`
`static double`	`ONE_OVER_PI`
`static double`	`ONE_THIRD`
`static double`	`PI`
`static double`	`PI_OVER_FOUR`
`static double`	`SQRT2`
`static double`	`SQRT2_INV`
`static double`	`SQRT3`
`static double`	`SQRT3_INV`
`static double`	`SQRT6`
`static double`	`TWO_OVER_PI`
`static double`	`TWO_PI`

Constructor Summary

Constructors
Constructor and Description

Math()

Constructors
Constructor and Description
`Math()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static double`	`abs(double a)`
`static double`	`acos(double a)`
`static double`	`asin(double a)`
`static double`	`asinc(double a)` Returns the inverse of the cardinal sine function of the given argument, i.e. the inverse of sin(x) / x.
`static double`	`asincP(double a)` Same as `asinc(double)` but assuming the argument is positive.
`static double`	`atan2(double y, double x)`
`static double`	`atanh(double x)` Returns tanh-1(x), i.e. the inverse function of tanh.
`static double`	`cos(double a)`
`static boolean`	`isFinite(double v)`
`static double`	`log(double x)`
`static double`	`oneMinusSin(double a)` To be used when sin(a) is near from 1 and a high precision is needed on 1 - sin(a).
`static double`	`pow(double a, double b)`
`static int`	`roots(double q0, double q1, double q2, double[] result)` Compute the number of real roots of the quadratic equation: q2x^2 + q1x + q0 = 0
`static int`	`roots(double q0, double q1, double q2, double q3, double[] result)`
`static long`	`round(double a)`
`static int`	`round(float a)`
`static double`	`signum(double a)`
`static double`	`sin(double a)`
`static double`	`sinc(double a)` Returns the cardinal sine function of the given angle, i.e. sin(x) / x.
`static double`	`sincP(double a)` Same as `sinc(double)` but assuming the argument is positive.
`static double`	`sqrt(double angleRadians)`
`static double`	`sqrtOfOneMinusSin(double a)` To be used when sin(a) is near from 1 and a high precision is needed on sqrt(1 - sin(a)).
`static double`	`sqrtOfOneMinusSinPC(double a)` Same as `sqrtOfOneMinusSin(double)` but limited to angle having a positive cosine (in practice cos(a/2 + PI/2) must be positive).
`static double`	`tan(double a)`
`static double`	`tanh(double x)`
`static double`	`toDegrees(double a)`
`static double`	`toRadians(double a)`

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - EPSILON
```
public static final double EPSILON
```
    See Also:
    
    Constant Field Values
  - ONE_THIRD
```
public static final double ONE_THIRD
```
    See Also:
    
    Constant Field Values
  - ONE_FOURTH
```
public static final double ONE_FOURTH
```
    See Also:
    
    Constant Field Values
  - PI
```
public static final double PI
```
    See Also:
    
    Constant Field Values
  - HALF_PI
```
public static final double HALF_PI
```
    See Also:
    
    Constant Field Values
  - PI_OVER_FOUR
```
public static final double PI_OVER_FOUR
```
    See Also:
    
    Constant Field Values
  - TWO_PI
```
public static final double TWO_PI
```
    See Also:
    
    Constant Field Values
  - ONE_OVER_PI
```
public static final double ONE_OVER_PI
```
    See Also:
    
    Constant Field Values
  - ONE_OVER_2PI
```
public static final double ONE_OVER_2PI
```
    See Also:
    
    Constant Field Values
  - TWO_OVER_PI
```
public static final double TWO_OVER_PI
```
    See Also:
    
    Constant Field Values
  - FOUR_OVER_PI
```
public static final double FOUR_OVER_PI
```
    See Also:
    
    Constant Field Values
  - LOG2
```
public static final double LOG2
```
  - SQRT2
```
public static final double SQRT2
```
  - SQRT2_INV
```
public static final double SQRT2_INV
```
  - SQRT3
```
public static final double SQRT3
```
  - SQRT3_INV
```
public static final double SQRT3_INV
```
  - SQRT6
```
public static final double SQRT6
```
- Constructor Detail
  - Math
```
public Math()
```
- Method Detail
  - isFinite
```
public static boolean isFinite(double v)
```
  - toRadians
```
public static double toRadians(double a)
```
  - toDegrees
```
public static double toDegrees(double a)
```
  - abs
```
public static double abs(double a)
```
  - signum
```
public static double signum(double a)
```
  - round
```
public static int round(float a)
```
  - round
```
public static long round(double a)
```
  - pow
```
public static double pow(double a,
                         double b)
```
  - cos
```
public static double cos(double a)
```
  - sin
```
public static double sin(double a)
```
  - oneMinusSin
```
public static double oneMinusSin(double a)
```
    To be used when sin(a) is near from 1 and a high precision is needed on 1 - sin(a). Uses formula: 2 * cos(x / 2 + pi/4) Coming from: 1 - sin(x) = sin(pi / 2) - sin(x) = 2 sin(pi / 4 - x / 2) cos(pi / 4 + x / 2) = -2 sin(x / 2 - pi / 4) cos(x / 2 + pi / 4) = -2 sin(x / 2 + pi / 4 - pi / 2) cos(x / 2 + pi / 4) = 2 cos(x / 2 + pi / 4) cos(x / 2 + pi / 4)
    
    Parameters:
    
    a - angle in radians
    
    Returns:
    
    1 - sin(a)
  - sqrtOfOneMinusSin
```
public static double sqrtOfOneMinusSin(double a)
```
    To be used when sin(a) is near from 1 and a high precision is needed on sqrt(1 - sin(a)). oneMinusSin(double).
    
    Parameters:
    
    a - angle in radians HAVING a POSITIVE COSINE.
    
    Returns:
    
    sqrt(1 - sin(a))
  - sqrtOfOneMinusSinPC
```
public static double sqrtOfOneMinusSinPC(double a)
```
    Same as sqrtOfOneMinusSin(double) but limited to angle having a positive cosine (in practice cos(a/2 + PI/2) must be positive).
    
    Parameters:
    
    a - angle in radians HAVING a POSITIVE COSINE, or more generally, a in [-3pi/2, pi/2].
    
    Returns:
    
    sqrt(1 - sin(a))
  - tan
```
public static double tan(double a)
```
  - sinc
```
public static double sinc(double a)
```
    Returns the cardinal sine function of the given angle, i.e. sin(x) / x. Precision of 10e-16 on small angles.
    
    Parameters:
    
    a - angle in radians
    
    Returns:
    
    the cardinal sine function of the given angle, i.e. sin(x) / x.
  - sincP
```
public static double sincP(double a)
```
    Same as sinc(double) but assuming the argument is positive. Precision of 10e-16 on small angles.
    
    Parameters:
    
    a - angle we are looking for the sine, must be > 0.
    
    Returns:
    
    the cardinal sine function of the given angle, assuming it is positive.
  - acos
```
public static double acos(double a)
```
  - asin
```
public static double asin(double a)
```
  - asinc
```
public static double asinc(double a)
```
    Returns the inverse of the cardinal sine function of the given argument, i.e. the inverse of sin(x) / x.
    
    Parameters:
    
    a - argument
    
    Returns:
    
    the inverse of the cardinal sine function of the given aegument.
  - asincP
```
public static double asincP(double a)
```
    Same as asinc(double) but assuming the argument is positive.
    
    Parameters:
    
    a - argument
    
    Returns:
    
    the inverse of the cardinal sine function of the given aegument, assuming the argument is positive.
  - atan2
```
public static double atan2(double y,
                           double x)
```
  - tanh
```
public static double tanh(double x)
```
  - atanh
```
public static double atanh(double x)
```
    Returns tanh-1(x), i.e. the inverse function of tanh.
    
    Parameters:
    
    x - argument, in range ]-1, 1[ (NaN returned otherwise)
    
    Returns:
    
    the hyperbolic inverse tangent of the given argument
  - log
```
public static double log(double x)
```
  - sqrt
```
public static double sqrt(double angleRadians)
```
  - roots
```
public static int roots(double q0,
                        double q1,
                        double q2,
                        double[] result)
```
    Compute the number of real roots of the quadratic equation: q2*x^2 + q1*x + q0 = 0
    
    Parameters:
    
    q0 - coefficient of x^0
    
    q1 - coefficient of x^1
    
    q2 - coefficient of x^2
    
    result - arrays of size at least 2 storing the real roots (if any)
    
    Returns:
    
    the number of real roots
  - roots
```
public static int roots(double q0,
                        double q1,
                        double q2,
                        double q3,
                        double[] result)
```

Class Math

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

EPSILON

ONE_THIRD

ONE_FOURTH

PI

HALF_PI

PI_OVER_FOUR

TWO_PI

ONE_OVER_PI

ONE_OVER_2PI

TWO_OVER_PI

FOUR_OVER_PI

LOG2

SQRT2

SQRT2_INV

SQRT3

SQRT3_INV

SQRT6

Constructor Detail

Math

Method Detail

isFinite

toRadians

toDegrees

abs

signum

round

round

pow

cos

sin

oneMinusSin

sqrtOfOneMinusSin

sqrtOfOneMinusSinPC

tan

sinc

sincP

acos

asin

asinc

asincP

atan2

tanh

atanh

log

sqrt

roots

roots