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

```
public final class MathFunctions
extends java.lang.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:

6.1.0

Field Summary

Fields
Modifier and Type Field Description

private static java.text.DecimalFormat DECIMAL_FORMAT

private static int MAX_RECURSION_CALLS

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
`private static double`	`continuedPolynomial(int n, double[] x)`	Private function calculating continued polynomial recursively.
`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 anyValue)`	For very small number returns the position of first significant digit, ie 0.1 = 1, 0.01 = 2
`static int`	`decimalNumberLength(double value)`	Length of a number represented in a standard decimal format
`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`	`divQuotient(double a, double b)`	Integer division (also called quotient) 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
`private static double`	`eulerNumber(int n, int k, int recursionCall)`
`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`	`factorialFalling(double x, double n)`	Falling factorial polynomial
`static double`	`factorialRising(double x, double n)`	Rising factorial polynomial
`static double`	`fibonacciNumber(double n)`	Fibonacci numbers
`static double`	`fibonacciNumber(int n)`	Fibonacci numbers
`private static double`	`fibonacciNumber(int n, int recursionCall)`
`static double`	`floor(double a)`	Floor function.
`static int`	`fractionalPartLength(double value)`	Fractional part length of a number represented in a standard decimal format
`static double`	`getFunctionValue(Expression f, Argument x, double x0)`	Calculates function f(x0) (given as expression) assigning Argument x = x0;
`static double[]`	`getFunctionValues(Expression f, Argument index, double from, double to, double delta)`	Returns array of double values of the function f(i) calculated on the range: i = from to i = to by step = delta
`static double`	`harmonicNumber(double n)`	Harmonic number
`static double`	`harmonicNumber(double x, double n)`	Harmonic number 1/1 + 1/2^x + ...
`static double`	`harmonicNumber(double x, int n)`	Harmonic number 1/1 + 1/2^x + ...
`static double`	`harmonicNumber(int n)`	Harmonic numer
`static double`	`integerPart(double x)`	Returns integer part of a double value.
`private static double`	`intIfAlmostIntOtherwiseOrig(double val)`	If double is almost integer returns the closes integer, otherwise original 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`	`lengthRound(double value)`	Intelligent rounding of a number within the decimal position of the ULP (Unit in the Last Place), provided that the result is significantly shortened in the standard decimal notation.
`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
`private static double`	`lucasNumber(int n, int recursionCall)`
`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
`private static double`	`powInt(double a, int n)`	Applies the integer exponent to the base a
`static double`	`rad(double a)`	Degrees to radius translation.
`private static void`	`refreshMaxAllowedRecursionDepth()`
`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
`private static double`	`Stirling1Number(int n, int k, int recursionCall)`
`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
`private static double`	`Stirling2Number(int n, int k, int recursionCall)`
`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

- Field Detail
  - MAX_RECURSION_CALLS
```
private static int MAX_RECURSION_CALLS
```
  - DECIMAL_FORMAT
```
private static final java.text.DecimalFormat DECIMAL_FORMAT
```
- Constructor Detail
  - MathFunctions
```
public MathFunctions()
```
- Method Detail
  - refreshMaxAllowedRecursionDepth
```
private static void refreshMaxAllowedRecursionDepth()
```
  - plus
```
public static 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 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 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 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
  - divQuotient
```
public static double divQuotient(double a,
                                 double b)
```
    Integer division (also called quotient) a / b applying canonical rounding if canonical rounding is enabled
    
    Parameters:
    
    a - The a parameter
    
    b - The b parameter
    
    Returns:
    
    The result of integer division
  - bellNumber
```
public static double bellNumber(int n)
```
    Bell Numbers
    
    Parameters:
    
    n - the n
    
    Returns:
    
    if n >= 0 returns Bell numbers, otherwise returns Double.NaN.
  - bellNumber
```
public static 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 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. Returns also Double.NaN when MAX RECURSION CALLS is exceeded.
    
    See Also:
    
    mXparser.getMaxAllowedRecursionDepth(), mXparser.setMaxAllowedRecursionDepth(int)
  - eulerNumber
```
private static double eulerNumber(int n,
                                  int k,
                                  int recursionCall)
```
  - eulerNumber
```
public static 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 double factorial(int n)
```
    Factorial
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    Factorial if n >=0, otherwise returns Double.NaN.
  - factorial
```
public static 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.
  - factorialFalling
```
public static double factorialFalling(double x,
                                      double n)
```
    Falling factorial polynomial
    
    Parameters:
    
    x - Argument
    
    n - Polynomial degree
    
    Returns:
    
    Falling factorial polynomial of degree n at point x
  - factorialRising
```
public static double factorialRising(double x,
                                     double n)
```
    Rising factorial polynomial
    
    Parameters:
    
    x - Argument
    
    n - Polynomial degree
    
    Returns:
    
    Rising factorial polynomial of degree n at point x
  - binomCoeff
```
public static 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 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 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 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 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 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 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 Returns also Double.NaN when MAX RECURSION CALLS is exceeded.
    
    See Also:
    
    mXparser.getMaxAllowedRecursionDepth(), mXparser.setMaxAllowedRecursionDepth(int)
  - Stirling1Number
```
private static double Stirling1Number(int n,
                                      int k,
                                      int recursionCall)
```
  - Stirling1Number
```
public static 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 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 Returns also Double.NaN when MAX RECURSION CALLS is exceeded.
    
    See Also:
    
    mXparser.getMaxAllowedRecursionDepth(), mXparser.setMaxAllowedRecursionDepth(int)
  - Stirling2Number
```
private static double Stirling2Number(int n,
                                      int k,
                                      int recursionCall)
```
  - Stirling2Number
```
public static 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 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 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 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 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 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 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 double catalanNumber(int n)
```
    Catalan numbers
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    Catalan numbers
  - catalanNumber
```
public static 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 double fibonacciNumber(int n)
```
    Fibonacci numbers
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n >= 0 returns fibonacci numbers, otherwise returns Double.NaN. Returns also Double.NaN when MAX RECURSION CALLS is exceeded.
    
    See Also:
    
    mXparser.getMaxAllowedRecursionDepth(), mXparser.setMaxAllowedRecursionDepth(int)
  - fibonacciNumber
```
private static double fibonacciNumber(int n,
                                      int recursionCall)
```
  - fibonacciNumber
```
public static 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 double lucasNumber(int n)
```
    Lucas numebrs
    
    Parameters:
    
    n - the n function parameter
    
    Returns:
    
    if n >= 0 returns Lucas numbers, otherwise returns Double.NaN. Returns also Double.NaN when MAX RECURSION CALLS is exceeded.
    
    See Also:
    
    mXparser.getMaxAllowedRecursionDepth(), mXparser.setMaxAllowedRecursionDepth(int)
  - lucasNumber
```
private static double lucasNumber(int n,
                                  int recursionCall)
```
  - lucasNumber
```
public static 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 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 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 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
```
private static double continuedPolynomial(int n,
                                          double[] x)
```
    Private function calculating continued polynomial recursively.
    
    Parameters:
    
    n - the polynomial order
    
    x - the x values
    
    Returns:
    
    continued polynomial value
  - continuedPolynomial
```
public static 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 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 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 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 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 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 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 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
  - powInt
```
private static double powInt(double a,
                             int n)
```
    Applies the integer exponent to the base a
    
    Parameters:
    
    a - The base
    
    n - The integer exponent
    
    Returns:
    
    Return a to the power of n, if canonical rounding is enable, the it operates on big numbers
  - power
```
public static 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 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 double tetration(double a,
                               double n)
```
    Tetration, exponential power, power series
    
    Parameters:
    
    a - base
    
    n - exponent
    
    Returns:
    
    Tetration result.
  - mod
```
public static 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 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 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 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 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 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 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.
  - intIfAlmostIntOtherwiseOrig
```
private static double intIfAlmostIntOtherwiseOrig(double val)
```
    If double is almost integer returns the closes integer, otherwise original value
    
    Parameters:
    
    val - Parameter
    
    Returns:
    
    f double is almost integer returns the closest integer, otherwise original value
  - asin
```
public static 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 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 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 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 double asec(double a)
```
    Arcus secant - inverse trigonometric secant function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    Inverse trigonometric secant function
  - acosec
```
public static double acosec(double a)
```
    Arcus cosecant - inverse trigonometric cosecant function
    
    Parameters:
    
    a - the a function parameter
    
    Returns:
    
    Inverse trigonometric cosecant function
  - ln
```
public static 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 double round(double value,
                           int places)
```
    Double rounding
    
    Parameters:
    
    value - double value to be rounded
    
    places - decimal places
    
    Returns:
    
    Rounded value
  - roundHalfUp
```
public static 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 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 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 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 int decimalDigitsBefore(double anyValue)
```
    For very small number returns the position of first significant digit, ie 0.1 = 1, 0.01 = 2
    
    Parameters:
    
    anyValue - Double value, small one.
    
    Returns:
    
    Number of digits, number of places.
  - ulp
```
public static 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 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.
  - decimalNumberLength
```
public static int decimalNumberLength(double value)
```
    Length of a number represented in a standard decimal format
    
    Parameters:
    
    value - A given number
    
    Returns:
    
    Length of a number represented in a standard decimal format including decimal separator, excluding leading zeros (integer part), excluding trailing zeros (fractional part)
  - fractionalPartLength
```
public static int fractionalPartLength(double value)
```
    Fractional part length of a number represented in a standard decimal format
    
    Parameters:
    
    value - A given number
    
    Returns:
    
    Fractional part length of a number represented in a standard decimal format excluding decimal separator, excluding trailing zeros (fractional part)
  - lengthRound
```
public static double lengthRound(double value)
```
    Intelligent rounding of a number within the decimal position of the ULP (Unit in the Last Place), provided that the result is significantly shortened in the standard decimal notation. Examples: 30.499999999999992 is rounded to 30.5, but 30.499999999999122 will not be rounded. Rounding is made to the decimal position of the ULP minus 2 on condition that the resulted number is shortened by at least 9 places.
    
    Parameters:
    
    value - A given number
    
    Returns:
    
    Returns an intelligently rounded number when the decimal position of ULP is a minimum of 11 and when rounded to the position of ULP - 2, shortens the number by a minimum of 9 places. Otherwise, returns original number.
  - coalesce
```
public static 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 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 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
  - getFunctionValue
```
public static double getFunctionValue(Expression f,
                                      Argument x,
                                      double x0)
```
    Calculates function f(x0) (given as expression) assigning Argument x = x0;
    
    Parameters:
    
    f - the expression
    
    x - the argument
    
    x0 - the argument value
    
    Returns:
    
    f.calculate()
    
    See Also:
    
    Expression
  - getFunctionValues
```
public static double[] getFunctionValues(Expression f,
                                         Argument index,
                                         double from,
                                         double to,
                                         double delta)
```
    Returns array of double values of the function f(i) calculated on the range: i = from to i = to by step = delta
    
    Parameters:
    
    f - Function expression
    
    index - Index argument
    
    from - 'from' value
    
    to - 'to' value
    
    delta - 'delta' step definition
    
    Returns:
    
    Array of function values

Modifier and Type	Field	Description
`private static java.text.DecimalFormat`	`DECIMAL_FORMAT`
`private static int`	`MAX_RECURSION_CALLS`

Class MathFunctions

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

MAX_RECURSION_CALLS

DECIMAL_FORMAT

Constructor Detail

MathFunctions

Method Detail

refreshMaxAllowedRecursionDepth

plus

minus

multiply

div

divQuotient

bellNumber

bellNumber

eulerNumber

eulerNumber

eulerNumber

factorial

factorial

factorialFalling

factorialRising

binomCoeff

binomCoeff

numberOfPermutations

numberOfPermutations

bernoulliNumber

bernoulliNumber

Stirling1Number

Stirling1Number

Stirling1Number

Stirling2Number

Stirling2Number

Stirling2Number

worpitzkyNumber

worpitzkyNumber

harmonicNumber

harmonicNumber

harmonicNumber

harmonicNumber

catalanNumber

catalanNumber

fibonacciNumber

fibonacciNumber

fibonacciNumber

lucasNumber

lucasNumber

lucasNumber

kroneckerDelta

kroneckerDelta

continuedFraction

continuedPolynomial

continuedPolynomial

eulerPolynomial

eulerPolynomial

chi

chi_LR

chi_L

chi_R

isAlmostInt

powInt

power

root

tetration

mod

sin

cos

tan

ctan

sec

cosec

intIfAlmostIntOtherwiseOrig

asin

acos

atan

actan