java.lang.Object
- org.mariuszgromada.math.mxparser.mathcollection.MathFunctions

```
public final class MathFunctions
extends Object
```
MathFunctions - the most popular math functions. Many of function implemented by this class could be found in java Math package (in fact functions from MathFunctions typically calls original functions from the Math package). The reason why it was "re-implemented" is: if you decide to implement your own function you do not need to change anything in the parser, jut modify function implementation in this class.

Version:

4.4.2

Author:

Mariusz Gromada
mariuszgromada.org@gmail.com
MathSpace.pl
MathParser.org - mXparser project page
mXparser on GitHub
mXparser on SourceForge
mXparser on Bitbucket
mXparser on CodePlex
Janet Sudoku - project web page
Janet Sudoku on GitHub
Janet Sudoku on CodePlex
Janet Sudoku on SourceForge
Janet Sudoku on BitBucket
Scalar Free
Scalar Pro
ScalarMath.org

Constructor Summary

Constructors
Constructor Description

MathFunctions()

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method	Description
`static double`	`abs(double a)`	Absolute value.
`static double`	`acos(double a)`	Arcus cosine - inverse trigonometric cosine function
`static double`	`acosec(double a)`	Arcus cosecant - inverse trigonometric cosecant function
`static double`	`actan(double a)`	Arcus cotangent - inverse trigonometric cotangent function
`static boolean`	`almostEqual(double a, double b)`	Check whether two double values are almost equal.
`static double`	`arcosh(double a)`	Arcus hyperbolic cosine - inverse hyperbolic cosine function.
`static double`	`arcoth(double a)`	Arcus hyperbolic tangent - inverse hyperbolic tangent function.
`static double`	`arcsch(double a)`	Arcus hyperbolic cosecant - inverse hyperbolic cosecant function.
`static double`	`arsech(double a)`	Arcus hyperbolic secant - inverse hyperbolic secant function.
`static double`	`arsinh(double a)`	Arcus hyperbolic sine - inverse hyperbolic sine function.
`static double`	`artanh(double a)`	Arcus hyperbolic tangent - inverse hyperbolic tangent function.
`static double`	`asec(double a)`	Arcus secant - inverse trigonometric secant function
`static double`	`asin(double a)`	Arcus sine - inverse trigonometric sine function
`static double`	`atan(double a)`	Arcus tangent - inverse trigonometric tangent function
`static double`	`bellNumber(double n)`	Bell number
`static double`	`bellNumber(int n)`	Bell Numbers
`static double`	`bernoulliNumber(double m, double n)`	Bernoulli numbers
`static double`	`bernoulliNumber(int m, int n)`	Bernoulli numbers
`static double`	`binomCoeff(double n, double k)`	Generalized binomial coefficient
`static double`	`binomCoeff(double n, long k)`	Generalized binomial coefficient
`static double`	`catalanNumber(double n)`	Catalan numbers
`static double`	`catalanNumber(int n)`	Catalan numbers
`static double`	`ceil(double a)`	Ceiling function.
`static double`	`chi(double x, double a, double b)`	Characteristic function x in (a,b)
`static double`	`chi_L(double x, double a, double b)`	Characteristic function x in [a,b)
`static double`	`chi_LR(double x, double a, double b)`	Characteristic function x in [a,b]
`static double`	`chi_R(double x, double a, double b)`	Characteristic function x in (a,b]
`static double`	`coalesce(double[] values)`	Returns the first non-NaN value
`static double`	`continuedFraction(double... sequence)`	Continued fraction
`static double`	`continuedPolynomial(double... x)`	Continued polynomial
`static double`	`cos(double a)`	Cosine trigonometric function
`static double`	`cosec(double a)`	Cosecant trigonometric function
`static double`	`cosh(double a)`	Hyperbolic cosine function.
`static double`	`coth(double a)`	Hyperbolic cotangent function.
`static double`	`csch(double a)`	Hyperbolic cosecant function.
`static double`	`ctan(double a)`	Cotangent trigonometric function
`static int`	`decimalDigitsBefore(double value)`	For very small number returns the position of first significant digit, ie 0.1 = 1, 0.01 = 2
`static double`	`deg(double a)`	Radius to degrees translation.
`static double`	`div(double a, double b)`	Division a / b applying canonical rounding if canonical rounding is enabled
`static double`	`eulerNumber(double n, double k)`	Euler numbers
`static double`	`eulerNumber(int n, int k)`	Euler numbers
`static double`	`eulerPolynomial(double m, double x)`	Euler polynomial
`static double`	`eulerPolynomial(int m, double x)`	Euler polynomial
`static double`	`exp(double a)`	Exponential function.
`static double`	`factorial(double n)`	Factorial
`static double`	`factorial(int n)`	Factorial
`static double`	`fibonacciNumber(double n)`	Fibonacci numbers
`static double`	`fibonacciNumber(int n)`	Fibonacci numbers
`static double`	`floor(double a)`	Floor function.
`static double`	`harmonicNumber(double n)`	Harmonic number
`static double`	`harmonicNumber(double x, double n)`	Harmonic number 1/1 + 1/2^x + ... + 1/n^x
`static double`	`harmonicNumber(double x, int n)`	Harmonic number 1/1 + 1/2^x + ... + 1/n^x
`static double`	`harmonicNumber(int n)`	Harmonic numer
`static double`	`integerPart(double x)`	Returns integer part of a double value.
`static boolean`	`isAlmostInt(double a)`	Verifies whether provided number is almost integer
`static boolean`	`isInteger(double x)`	Check whether double value is almost integer.
`static double`	`kroneckerDelta(double i, double j)`	Kronecker delta
`static double`	`kroneckerDelta(int i, int j)`	Kronecker delta
`static double`	`ln(double a)`	Natural logarithm
`static double`	`log(double a, double b)`	General logarithm.
`static double`	`log10(double a)`	Common logarithm
`static double`	`log2(double a)`	Binary logarithm
`static double`	`lucasNumber(double n)`	Lucas numebrs
`static double`	`lucasNumber(int n)`	Lucas numebrs
`static double`	`minus(double a, double b)`	Subtraction a - b applying canonical rounding if canonical rounding is enabled
`static double`	`mod(double a, double b)`	Modulo operator a % b
`static double`	`multiply(double a, double b)`	Multiplication a * b applying canonical rounding if canonical rounding is enabled
`static double`	`numberOfPermutations(double n, double k)`	Generalized coefficient returning number of k permutations that can be drawn for n elements set.
`static double`	`numberOfPermutations(double n, long k)`	Generalized coefficient returning number of k permutations that can be drawn for n elements set.
`static double`	`plus(double a, double b)`	Addition a + b applying canonical rounding if canonical rounding is enabled
`static double`	`power(double a, double b)`	Power function a^b
`static double`	`rad(double a)`	Degrees to radius translation.
`static double`	`root(double n, double x)`	Nth order root of a number
`static double`	`round(double value, int places)`	Double rounding
`static double`	`roundDown(double value, int places)`	Double down rounding
`static double`	`roundHalfUp(double value, int places)`	Double half up rounding
`static double`	`roundUlp(double number)`	Unit in the last place rounding, see 0.1 + 0.1 + 0.1 vs roundUlp(0.1 + 0.1 + 0.1)
`static double`	`sa(double a)`	Normalized sinc function.
`static double`	`sec(double a)`	Secant trigonometric function
`static double`	`sech(double a)`	Hyperbolic secant function.
`static double`	`sgn(double a)`	Signum function.
`static double`	`sin(double a)`	Sine trigonometric function
`static double`	`sinc(double a)`	Sinc function.
`static double`	`sinh(double a)`	Hyperbolic sine function.
`static double`	`sqrt(double a)`	Square root.
`static double`	`Stirling1Number(double n, double k)`	Stirling numbers of the first kind
`static double`	`Stirling1Number(int n, int k)`	Stirling numbers of the first kind
`static double`	`Stirling2Number(double n, double k)`	Stirling numbers of the second kind
`static double`	`Stirling2Number(int n, int k)`	Stirling numbers of the second kind
`static double`	`tan(double a)`	Tangent trigonometric function
`static double`	`tanh(double a)`	Hyperbolic tangent function.
`static double`	`tetration(double a, double n)`	Tetration, exponential power, power series
`static double`	`ulp(double value)`	Unit in the last place(ULP) for double
`static int`	`ulpDecimalDigitsBefore(double value)`	Unit in The Last Place - number of decimal digits before
`static double`	`worpitzkyNumber(double n, double k)`	Worpitzky numbers
`static double`	`worpitzkyNumber(int n, int k)`	Worpitzky numbers

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

- Constructor Detail
  - MathFunctions
```
public MathFunctions()
```
- Method Detail
  - plus
```
public static final double plus(double a,
                                double b)
```
    Addition a + b applying canonical rounding if canonical rounding is enabled
    
    Parameters:
    
    a - The a parameter
    
    b - The b parameter
    
    Returns:
    
    The result of addition
  - minus
```
public static final double minus(double a,
                                 double b)
```
    Subtraction a - b applying canonical rounding if canonical rounding is enabled
    
    Parameters:
    
    a - The a parameter
    
    b - The b parameter
    
    Returns:
    
    The result of subtraction
  - multiply
```
public static final double multiply(double a,
                                    double b)
```
    Multiplication a * b applying canonical rounding if canonical rounding is enabled
    
    Parameters:
    
    a - The a parameter
    
    b - The b parameter
    
    Returns:
    
    The result of multiplication
  - div
```
public static final double div(double a,
                               double b)
```
    Division a / b applying canonical rounding if canonical rounding is enabled
    
    Parameters:
    
    a - The a parameter
    
    b - The b parameter
    
    Returns:
    
    The result of division
  - bellNumber
```
public static final double bellNumber(int n)
```
    Bell Numbers
    
    Parameters:
    
    n - the n
    
    Returns:
    
    if n >= 0 returns Bell numbers, otherwise returns Double.NaN.
  - bellNumber
```
public static final double bellNumber(double n)
```
    Bell number
    
    Parameters:
    
    n - the n
    
    Returns:
    
    if n <> Double.NaN return bellNumber( (int)Math.round(n) ), otherwise return Double.NaN.
  - eulerNumber
```
public static final double eulerNumber(int n,
                                       int k)
```
    Euler numbers
    
    Parameters:
    
    n - the n function param
    
    k - the k function param
    
    Returns:
    
    if n >=0 returns Euler number, otherwise return Double.NaN.
  - eulerNumber
```
public static final double eulerNumber(double n,
                                       double k)
```
    Euler numbers
    
    Parameters:
    
    n - the n function param
    
    k - the k function param
    
    Returns:
    
    if n, k <> Double.NaN returns eulerNumber( (int)Math.round(n), (int)Math.round(k) ), otherwise return Double.NaN.
  - factorial
```
public static final double factorial(int n)
```
    Factorial
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    Factorial if n >=0, otherwise returns Double.NaN.
  - factorial
```
public static final double factorial(double n)
```
    Factorial
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n <> Double.NaN return factorial( (int)Math.round(n) ), otherwise returns Double.NaN.
  - binomCoeff
```
public static final double binomCoeff(double n,
                                      long k)
```
    Generalized binomial coefficient
    
    Parameters:
    
    n - the n function parameter
    
    k - k the k function parameter
    
    Returns:
    
    Generalized binomial coefficient, if n = Double.NaN or k < 0 returns Double.NaN.
  - binomCoeff
```
public static final double binomCoeff(double n,
                                      double k)
```
    Generalized binomial coefficient
    
    Parameters:
    
    n - the n function parameter
    
    k - the k function parameter
    
    Returns:
    
    if n, k <> Double.NaN returns binomCoeff(n, (int)Math.round(k) ), otherwise returns Double.NaN.
  - numberOfPermutations
```
public static final double numberOfPermutations(double n,
                                                long k)
```
    Generalized coefficient returning number of k permutations that can be drawn for n elements set.
    
    Parameters:
    
    n - the n function parameter
    
    k - the k function parameter
    
    Returns:
    
    For k greater than 0 return number of permutations, otherwise returns Double.NaN
  - numberOfPermutations
```
public static final double numberOfPermutations(double n,
                                                double k)
```
    Generalized coefficient returning number of k permutations that can be drawn for n elements set.
    
    Parameters:
    
    n - the n function parameter
    
    k - the k function parameter
    
    Returns:
    
    For k greater than 0 return number of permutations, otherwise returns Double.NaN
  - bernoulliNumber
```
public static final double bernoulliNumber(int m,
                                           int n)
```
    Bernoulli numbers
    
    Parameters:
    
    m - the m function parameter
    
    n - the n function parameter
    
    Returns:
    
    if n, m >= 0 returns Bernoulli number, otherwise returns Double.NaN.
  - bernoulliNumber
```
public static final double bernoulliNumber(double m,
                                           double n)
```
    Bernoulli numbers
    
    Parameters:
    
    m - the m function parameter
    
    n - the n function parameter
    
    Returns:
    
    if n, m <> Double.NaN returns bernoulliNumber( (int)Math.round(m), (int)Math.round(n) ), otherwise returns Double.NaN.
  - Stirling1Number
```
public static final double Stirling1Number(int n,
                                           int k)
```
    Stirling numbers of the first kind
    
    Parameters:
    
    n - the n function parameter
    
    k - the k function parameter
    
    Returns:
    
    Stirling numbers of the first kind
  - Stirling1Number
```
public static final double Stirling1Number(double n,
                                           double k)
```
    Stirling numbers of the first kind
    
    Parameters:
    
    n - the n function parameter
    
    k - the k function parameter
    
    Returns:
    
    if n, k <> Doube.NaN returns Stirling1Number( (int)Math.round(n), (int)Math.round(k) ), otherwise returns Double.NaN.
  - Stirling2Number
```
public static final double Stirling2Number(int n,
                                           int k)
```
    Stirling numbers of the second kind
    
    Parameters:
    
    n - the n function parameter
    
    k - the k function parameter
    
    Returns:
    
    Stirling numbers of the second kind
  - Stirling2Number
```
public static final double Stirling2Number(double n,
                                           double k)
```
    Stirling numbers of the second kind
    
    Parameters:
    
    n - the n function parameter
    
    k - the k function parameter
    
    Returns:
    
    if n, k <> Doube.NaN returns Stirling2Number( (int)Math.round(n), (int)Math.round(k) ), otherwise returns Double.NaN.
  - worpitzkyNumber
```
public static final double worpitzkyNumber(int n,
                                           int k)
```
    Worpitzky numbers
    
    Parameters:
    
    n - the n function parameter
    
    k - the k function parameter
    
    Returns:
    
    if n,k >= 0 and k <= n return Worpitzky number, otherwise return Double.NaN.
  - worpitzkyNumber
```
public static final double worpitzkyNumber(double n,
                                           double k)
```
    Worpitzky numbers
    
    Parameters:
    
    n - the n function parameter
    
    k - the k function parameter
    
    Returns:
    
    if n,k <> Double.NaN returns worpitzkyNumber( (int)Math.round(n), (int)Math.round(k) ), otherwise return Double.NaN.
  - harmonicNumber
```
public static final double harmonicNumber(int n)
```
    Harmonic numer
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n > 0 returns harmonic number, otherwise returns 0 (empty summation operator)
  - harmonicNumber
```
public static final double harmonicNumber(double n)
```
    Harmonic number
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n <> Double.NaN returns harmonicNumber( (int)Math.round(n) ), otherwise returns Double.NaN
  - harmonicNumber
```
public static final double harmonicNumber(double x,
                                          int n)
```
    Harmonic number 1/1 + 1/2^x + ... + 1/n^x
    
    Parameters:
    
    x - the x function parameter
    
    n - the n function parameter
    
    Returns:
    
    if x <> Double.NaN and x >= 0 Harmonic number, otherwise returns Double.NaN.
  - harmonicNumber
```
public static final double harmonicNumber(double x,
                                          double n)
```
    Harmonic number 1/1 + 1/2^x + ... + 1/n^x
    
    Parameters:
    
    x - the x function parameter
    
    n - the n function parameter
    
    Returns:
    
    if x,n <> Double.NaN returns harmonicNumber( x, (int)Math.round(n) ), otherwise returns Double.NaN.
  - catalanNumber
```
public static final double catalanNumber(int n)
```
    Catalan numbers
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    Catalan numbers
  - catalanNumber
```
public static final double catalanNumber(double n)
```
    Catalan numbers
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n <> Double.NaN returns catalanNumber( (int)Math.round(n) ), otherwise returns Double.NaN.
  - fibonacciNumber
```
public static final double fibonacciNumber(int n)
```
    Fibonacci numbers
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n >= 0 returns fibonacci numbers, otherwise returns Double.NaN.
  - fibonacciNumber
```
public static final double fibonacciNumber(double n)
```
    Fibonacci numbers
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n <> Double.NaN returns fibonacciNumber( (int)Math.round(n) ), otherwise returns Double.NaN.
  - lucasNumber
```
public static final double lucasNumber(int n)
```
    Lucas numebrs
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n >= 0 returns Lucas numbers, otherwise returns Double.NaN.
  - lucasNumber
```
public static final double lucasNumber(double n)
```
    Lucas numebrs
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n <> Double.NaN returns lucasNumber( (int)Math.round(n) ), otherwise returns Double.NaN.
  - kroneckerDelta
```
public static final double kroneckerDelta(double i,
                                          double j)
```
    Kronecker delta
    
    Parameters:
    
    i - the i function parameter
    
    j - the j function parameter
    
    Returns:
    
    if i,j <> Double.NaN returns Kronecker delta, otherwise returns Double.NaN.
  - kroneckerDelta
```
public static final double kroneckerDelta(int i,
                                          int j)
```
    Kronecker delta
    
    Parameters:
    
    i - the i function parameter
    
    j - the j function parameter
    
    Returns:
    
    Kronecker delta
  - continuedFraction
```
public static final double continuedFraction(double... sequence)
```
    Continued fraction
    
    Parameters:
    
    sequence - the numbers
    
    Returns:
    
    if each number form the sequence <> Double.NaN and there is no division by 0 while computing returns continued fraction value, otherwise returns Double.NaN.
  - continuedPolynomial
```
public static final double continuedPolynomial(double... x)
```
    Continued polynomial
    
    Parameters:
    
    x - the x values
    
    Returns:
    
    if each number for x is different the Double.NaN returns continued polynomial, otherwise returns Double.NaN.
  - eulerPolynomial
```
public static final double eulerPolynomial(int m,
                                           double x)
```
    Euler polynomial
    
    Parameters:
    
    m - the m parameter
    
    x - the x parameter
    
    Returns:
    
    if x <> Double.NaN and m >= 0 returns polynomial value, otherwise returns Double.NaN.
  - eulerPolynomial
```
public static final double eulerPolynomial(double m,
                                           double x)
```
    Euler polynomial
    
    Parameters:
    
    m - the m parameter
    
    x - the x parameter
    
    Returns:
    
    if x,m <> Double.NaN returns eulerPolynomial( (int)Math.round(m), (int)Math.round(x) ), otherwise returns Double.NaN.
  - chi
```
public static final double chi(double x,
                               double a,
                               double b)
```
    Characteristic function x in (a,b)
    
    Parameters:
    
    x - the x value
    
    a - the left (lower) limit
    
    b - the right (upper) limit
    
    Returns:
    
    if x, a, b <> Double.NaN returns characteristic function value on the (a,b) range.
  - chi_LR
```
public static final double chi_LR(double x,
                                  double a,
                                  double b)
```
    Characteristic function x in [a,b]
    
    Parameters:
    
    x - the x value
    
    a - the left (lower) limit
    
    b - the right (upper) limit
    
    Returns:
    
    if x, a, b <> Double.NaN returns characteristic function value on the [a,b] range.
  - chi_L
```
public static final double chi_L(double x,
                                 double a,
                                 double b)
```
    Characteristic function x in [a,b)
    
    Parameters:
    
    x - the x value
    
    a - the left (lower) limit
    
    b - the right (upper) limit
    
    Returns:
    
    if x, a, b <> Double.NaN returns characteristic function value on the [a,b) range.
  - chi_R
```
public static final double chi_R(double x,
                                 double a,
                                 double b)
```
    Characteristic function x in (a,b]
    
    Parameters:
    
    x - the x value
    
    a - the left (lower) limit
    
    b - the right (upper) limit
    
    Returns:
    
    if x, a, b <> Double.NaN returns characteristic function value on the (a,b] range.
  - isAlmostInt
```
public static final boolean isAlmostInt(double a)
```
    Verifies whether provided number is almost integer
    
    Parameters:
    
    a - The number to be verified
    
    Returns:
    
    True if the number is almost integer according to the default epsilon, otherwise returns false.
    
    See Also:
    
    BinaryRelations.DEFAULT_COMPARISON_EPSILON
  - power
```
public static final double power(double a,
                                 double b)
```
    Power function a^b
    
    Parameters:
    
    a - the a function parameter
    
    b - the b function parameter
    
    Returns:
    
    if a,b <> Double.NaN returns Math.pow(a, b), otherwise returns Double.NaN.
  - root
```
public static final double root(double n,
                                double x)
```
    Nth order root of a number
    
    Parameters:
    
    n - Root order
    
    x - Number
    
    Returns:
    
    Returns root of a number. If calculation is not possible Double.NaN is returned.
  - tetration
```
public static final double tetration(double a,
                                     double n)
```
    Tetration, exponential power, power series
    
    Parameters:
    
    a - base
    
    n - exponent
    
    Returns:
    
    Tetration result.
  - mod
```
public static final double mod(double a,
                               double b)
```
    Modulo operator a % b
    
    Parameters:
    
    a - the a function parameter
    
    b - the b function parameter
    
    Returns:
    
    if a,b <> Double.NaN returns a % b.
  - sin
```
public static final double sin(double a)
```
    Sine trigonometric function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN return Math.sin(a), otherwise return Double.NaN.
  - cos
```
public static final double cos(double a)
```
    Cosine trigonometric function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.cos(a), otherwise returns Double.NaN.
  - tan
```
public static final double tan(double a)
```
    Tangent trigonometric function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.tan(a), otherwise returns Double.NaN.
  - ctan
```
public static final double ctan(double a)
```
    Cotangent trigonometric function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and tan(a) <> 0 returns 1 / Math.tan(a), otherwise returns Double.NaN.
  - sec
```
public static final double sec(double a)
```
    Secant trigonometric function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and cos(a) <> 0 returns 1 / Math.cos(a), otherwise returns Double.NaN.
  - cosec
```
public static final double cosec(double a)
```
    Cosecant trigonometric function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and sin(a) <> 0 returns 1 / Math.sin(a), otherwise returns Double.NaN.
  - asin
```
public static final double asin(double a)
```
    Arcus sine - inverse trigonometric sine function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.asin(a), otherwise returns Double.NaN.
  - acos
```
public static final double acos(double a)
```
    Arcus cosine - inverse trigonometric cosine function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.acos(a), otherwise returns Double.NaN.
  - atan
```
public static final double atan(double a)
```
    Arcus tangent - inverse trigonometric tangent function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.atan(a), otherwise returns Double.NaN.
  - actan
```
public static final double actan(double a)
```
    Arcus cotangent - inverse trigonometric cotangent function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and a <> 0 returns Math.atan(1/a), otherwise returns Double.NaN.
  - asec
```
public static final double asec(double a)
```
    Arcus secant - inverse trigonometric secant function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    Inverse trigonometric secant function
  - acosec
```
public static final double acosec(double a)
```
    Arcus cosecant - inverse trigonometric cosecant function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    Inverse trigonometric cosecant function
  - ln
```
public static final double ln(double a)
```
    Natural logarithm
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.log(1/a), otherwise returns Double.NaN.
  - log2
```
public static final double log2(double a)
```
    Binary logarithm
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.log(a)/Math.log(2.0), otherwise returns Double.NaN.
  - log10
```
public static final double log10(double a)
```
    Common logarithm
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.log10(a), otherwise returns Double.NaN.
  - rad
```
public static final double rad(double a)
```
    Degrees to radius translation.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.toRadians(a), otherwise returns Double.NaN.
  - exp
```
public static final double exp(double a)
```
    Exponential function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.exp(a), otherwise returns Double.NaN.
  - sqrt
```
public static final double sqrt(double a)
```
    Square root.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.sqrt(a), otherwise returns Double.NaN.
  - sinh
```
public static final double sinh(double a)
```
    Hyperbolic sine function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.sinh(a), otherwise returns Double.NaN.
  - cosh
```
public static final double cosh(double a)
```
    Hyperbolic cosine function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.cosh(a), otherwise returns Double.NaN.
  - tanh
```
public static final double tanh(double a)
```
    Hyperbolic tangent function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.tanh(a), otherwise returns Double.NaN.
  - coth
```
public static final double coth(double a)
```
    Hyperbolic cotangent function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and tanh(a) <> 0 returns 1 / Math.tanh(a), otherwise returns Double.NaN.
  - sech
```
public static final double sech(double a)
```
    Hyperbolic secant function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and cosh(a) <> 0 returns 1 / Math.cosh(a), otherwise returns Double.NaN.
  - csch
```
public static final double csch(double a)
```
    Hyperbolic cosecant function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and sinh(a) <> 0 returns 1 / Math.sinh(a), otherwise returns Double.NaN.
  - deg
```
public static final double deg(double a)
```
    Radius to degrees translation.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.toDegrees(a), otherwise returns Double.NaN.
  - abs
```
public static final double abs(double a)
```
    Absolute value.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.abs(a), otherwise returns Double.NaN.
  - sgn
```
public static final double sgn(double a)
```
    Signum function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.signum(a), otherwise returns Double.NaN.
  - floor
```
public static final double floor(double a)
```
    Floor function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.floor(a), otherwise returns Double.NaN.
  - ceil
```
public static final double ceil(double a)
```
    Ceiling function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.ceil(a), otherwise returns Double.NaN.
  - arsinh
```
public static final double arsinh(double a)
```
    Arcus hyperbolic sine - inverse hyperbolic sine function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.log(a + Math.sqrt(a*a+1)), otherwise returns Double.NaN.
  - arcosh
```
public static final double arcosh(double a)
```
    Arcus hyperbolic cosine - inverse hyperbolic cosine function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN returns Math.log(a + Math.sqrt(a*a-1)), otherwise returns Double.NaN.
  - artanh
```
public static final double artanh(double a)
```
    Arcus hyperbolic tangent - inverse hyperbolic tangent function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and 1-a <> 0 returns 0.5*Math.log( (1+a)/(1-a) ), otherwise returns Double.NaN.
  - arcoth
```
public static final double arcoth(double a)
```
    Arcus hyperbolic tangent - inverse hyperbolic tangent function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and a-1 <> 0 returns 0.5*Math.log( (a+1)/(a-1) );, otherwise returns Double.NaN.
  - arsech
```
public static final double arsech(double a)
```
    Arcus hyperbolic secant - inverse hyperbolic secant function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and a <> 0 returns Math.log( (1+Math.sqrt(1-a*a))/a);, otherwise returns Double.NaN.
  - arcsch
```
public static final double arcsch(double a)
```
    Arcus hyperbolic cosecant - inverse hyperbolic cosecant function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and a <> 0 returns Math.log( (1+Math.sqrt(1-a*a))/a);, otherwise returns Double.NaN.
  - sa
```
public static final double sa(double a)
```
    Normalized sinc function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and a <> 0 returns Math.sin(PI*a) / (PI*a);, otherwise returns Double.NaN.
  - sinc
```
public static final double sinc(double a)
```
    Sinc function.
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    if a <> Double.NaN and a <> 0 returns Math.sin(a) / (a), otherwise returns Double.NaN.
  - log
```
public static final double log(double a,
                               double b)
```
    General logarithm.
    
    Parameters:
    
    a - the a function parameter (base)
    
    b - the b function parameter (number)
    
    Returns:
    
    if a,b <> Double.NaN and log(b) <> 0 returns Math.log(a) / Math.log(b), otherwise returns Double.NaN.
  - round
```
public static final double round(double value,
                                 int places)
```
    Double rounding
    
    Parameters:
    
    value - double value to be rounded
    
    places - decimal places
    
    Returns:
    
    Rounded value
  - roundHalfUp
```
public static final double roundHalfUp(double value,
                                       int places)
```
    Double half up rounding
    
    Parameters:
    
    value - double value to be rounded
    
    places - decimal places
    
    Returns:
    
    Rounded value
  - roundDown
```
public static final double roundDown(double value,
                                     int places)
```
    Double down rounding
    
    Parameters:
    
    value - double value to be rounded
    
    places - decimal places
    
    Returns:
    
    Rounded value
  - roundUlp
```
public static final double roundUlp(double number)
```
    Unit in the last place rounding, see 0.1 + 0.1 + 0.1 vs roundUlp(0.1 + 0.1 + 0.1)
    
    Parameters:
    
    number - Double number that is to be rounded
    
    Returns:
    
    Double number with rounded ulp
    
    See Also:
    
    decimalDigitsBefore(double), ulp(double)
  - integerPart
```
public static final double integerPart(double x)
```
    Returns integer part of a double value.
    
    Parameters:
    
    x - Number
    
    Returns:
    
    For non- negative x returns Math.floor(x), otherwise returns -Math.floor(-x)
  - decimalDigitsBefore
```
public static final int decimalDigitsBefore(double value)
```
    For very small number returns the position of first significant digit, ie 0.1 = 1, 0.01 = 2
    
    Parameters:
    
    value - Double value, small one.
    
    Returns:
    
    Number of digits, number of places.
  - ulp
```
public static final double ulp(double value)
```
    Unit in the last place(ULP) for double
    
    Parameters:
    
    value - Double number
    
    Returns:
    
    ULP for a given double.
  - ulpDecimalDigitsBefore
```
public static final int ulpDecimalDigitsBefore(double value)
```
    Unit in The Last Place - number of decimal digits before
    
    Parameters:
    
    value - Double number
    
    Returns:
    
    Positive number of digits N for ulp = 1e-{N+1}, if ulp is > 1 then -1 is returned. Returned proper value is always between -1 and +322. If value is NaN then -2 is returned.
  - coalesce
```
public static final double coalesce(double[] values)
```
    Returns the first non-NaN value
    
    Parameters:
    
    values - List of values
    
    Returns:
    
    Returns the first non-NaN value, if list is null then returns Double.NaN, if list contains no elements then returns Double.NaN.
  - isInteger
```
public static final boolean isInteger(double x)
```
    Check whether double value is almost integer.
    
    Parameters:
    
    x - Number
    
    Returns:
    
    True if double value is almost integer, otherwise false. BinaryRelations.DEFAULT_COMPARISON_EPSILON
    
    See Also:
    
    BinaryRelations.DEFAULT_COMPARISON_EPSILON
  - almostEqual
```
public static final boolean almostEqual(double a,
                                        double b)
```
    Check whether two double values are almost equal.
    
    Parameters:
    
    a - First number
    
    b - Second number
    
    Returns:
    
    True if double values are almost equal, otherwise false. BinaryRelations.DEFAULT_COMPARISON_EPSILON
    
    See Also:
    
    BinaryRelations.DEFAULT_COMPARISON_EPSILON

Class MathFunctions

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

MathFunctions

Method Detail

plus

minus

multiply

div

bellNumber

bellNumber

eulerNumber

eulerNumber

factorial

factorial

binomCoeff

binomCoeff

numberOfPermutations

numberOfPermutations

bernoulliNumber

bernoulliNumber

Stirling1Number

Stirling1Number

Stirling2Number

Stirling2Number

worpitzkyNumber

worpitzkyNumber

harmonicNumber

harmonicNumber

harmonicNumber

harmonicNumber

catalanNumber

catalanNumber

fibonacciNumber

fibonacciNumber

lucasNumber

lucasNumber

kroneckerDelta

kroneckerDelta

continuedFraction

continuedPolynomial

eulerPolynomial

eulerPolynomial

chi

chi_LR

chi_L

chi_R

isAlmostInt

power

root

tetration

mod

sin

cos

tan

ctan

sec

cosec

asin

acos

atan

actan

asec

acosec

ln

log2

log10

rad

exp

sqrt

sinh

cosh

tanh

coth

sech

csch

deg

abs