Package org.mariuszgromada.math.mxparser.mathcollection

Class MathFunctions

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:
6.1.0
Author:
Mariusz Gromada
MathParser.org - mXparser project page
mXparser on GitHub
INFIMA place to purchase a commercial MathParser.org-mXparser software license
info@mathparser.org
ScalarMath.org - a powerful math engine and math scripting language
Scalar Lite
Scalar Pro
MathSpace.pl

  • Constructor Summary

    Constructors
    Constructor
    Description
    MathFunctions()
     

  • Method Summary

    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 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
    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
    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 + ... + 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
    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
    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 Details

    • MathFunctions

      public MathFunctions()

  • Method Details

    • 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:

    • 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:

    • 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:

    • 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:

    • 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:

    • 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

      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:

    • 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.

    • 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:

    • 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:

    • 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:

    • 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:

    • 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