# Class FixedPrecisionApfloatHelper

java.lang.Object
org.apfloat.FixedPrecisionApcomplexHelper
org.apfloat.FixedPrecisionApfloatHelper

public class FixedPrecisionApfloatHelper extends FixedPrecisionApcomplexHelper
Fixed-precision mathematical functions for floating-point numbers.

All results of the mathematical operations are set to have the specified precision. Also all input arguments are set to the specified precision before the operation. If the specified precision is not infinite, this helper class also avoids `InfiniteExpansionException` e.g. in case where it would happen with `ApfloatMath.acos(Apfloat.ZERO)`.

Since:
  1.5
Version:
  1.16.0
Author:
  Mikko Tommila

- ## Constructor Summary

  Constructors
  Constructor
  Description
  `FixedPrecisionApfloatHelper(long precision)`
  Constructs an apfloat fixed-precison helper with the specified precision.

- ## Method Summary

  Modifier and Type
  Method
  Description
  `Apfloat`
  `abs(Apfloat x)`
  Absolute value.
  `Apfloat`
  `acos(Apfloat x)`
  Arc cosine.
  `Apfloat`
  `acosh(Apfloat x)`
  Hyperbolic arc cosine.
  `Apfloat`
  `add(Apfloat x, Apfloat y)`
  Addition.
  `Apfloat`
  `agm(Apfloat a, Apfloat b)`
  Arithmetic-geometric mean.
  `Apfloat`
  `airyAi(Apfloat x)`
  Airy function Ai.
  `Apfloat`
  `airyAiPrime(Apfloat x)`
  Derivative of the Airy function Ai.
  `Apfloat`
  `airyBi(Apfloat x)`
  Airy function Bi.
  `Apfloat`
  `airyBiPrime(Apfloat x)`
  Derivative of the Airy function Bi.
  `Apfloat`
  `angerJ(Apfloat ν, Apfloat x)`
  Anger function 𝐉.
  `Apfloat`
  `asin(Apfloat x)`
  Arc sine.
  `Apfloat`
  `asinh(Apfloat x)`
  Hyperbolic arc sine.
  `Apfloat`
  `atan(Apfloat x)`
  Arc tangent.
  `Apfloat`
  `atan2(Apfloat x, Apfloat y)`
  Angle of point.
  `Apfloat`
  `atanh(Apfloat x)`
  Hyperbolic arc tangent.
  `Apfloat`
  `barnesG(Apfloat x)`
  Barnes G-function.
  `Apfloat`
  `bernoulliB(long n, Apfloat x)`
  Bernoulli polynomial.
  `Apfloat`
  `besselI(Apfloat ν, Apfloat x)`
  Modified Bessel function of the first kind.
  `Apfloat`
  `besselJ(Apfloat ν, Apfloat x)`
  Bessel function of the first kind.
  `Apfloat`
  `besselK(Apfloat ν, Apfloat x)`
  Modified Bessel function of the second kind.
  `Apfloat`
  `besselY(Apfloat ν, Apfloat x)`
  Bessel function of the second kind.
  `Apfloat`
  `beta(Apfloat a, Apfloat b)`
  Beta function.
  `Apfloat`
  `beta(Apfloat x, Apfloat a, Apfloat b)`
  Incomplete beta function.
  `Apfloat`
  `beta(Apfloat x1, Apfloat x2, Apfloat a, Apfloat b)`
  Generalized incomplete beta function.
  `Apfloat`
  `binomial(Apfloat n, Apfloat k)`
  Binomial coefficient.
  `Apfloat`
  `cbrt(Apfloat x)`
  Cube root.
  `Apfloat`
  `ceil(Apfloat x)`
  Ceiling function.
  `Apfloat`
  `chebyshevT(Apfloat ν, Apfloat x)`
  Chebyshev function of the first kind.
  `Apfloat`
  `chebyshevU(Apfloat ν, Apfloat x)`
  Chebyshev function of the second kind.
  `Apfloat`
  `clausenC(Apfloat s, Apfloat θ)`
  Clausen function C.
  `Apfloat`
  `clausenCl(long n, Apfloat θ)`
  Clausen function Cl.
  `Apfloat`
  `clausenS(Apfloat s, Apfloat θ)`
  Clausen function S.
  `Apfloat`
  `clausenSl(long n, Apfloat θ)`
  Clausen function Sl.
  `Apfloat[]`
  `continuedFraction(Apfloat x, int n)`
  Continued fraction.
  `Apfloat[]`
  `convergents(Apfloat x, int n)`
  Convergents.
  `Apfloat`
  `copySign(Apfloat x, Apfloat y)`
  Copies the sign from one number to another.
  `Apfloat`
  `cos(Apfloat x)`
  Cosine.
  `Apfloat`
  `cosh(Apfloat x)`
  Hyperbolic cosine.
  `Apfloat`
  `coshIntegral(Apfloat x)`
  Hyperbolic cosine integral.
  `Apfloat`
  `cosIntegral(Apfloat x)`
  Cosine integral.
  `Apfloat`
  `dawsonF(Apfloat x)`
  Dawson's integral F.
  `Apfloat`
  `digamma(Apfloat x)`
  Digamma function.
  `Apfloat`
  `divide(Apfloat x, Apfloat y)`
  Division.
  `Apfloat`
  `doubleFactorial(long n)`
  Double factorial.
  `Apfloat`
  `doubleFactorial(long n, int radix)`
  Double factorial.
  `Apfloat`
  `ellipticE(Apfloat x)`
  Complete elliptic integral of the second kind.
  `Apfloat`
  `ellipticK(Apfloat x)`
  Complete elliptic integral of the first kind.
  `Apfloat`
  `erf(Apfloat x)`
  Error function.
  `Apfloat`
  `erfc(Apfloat x)`
  Complementary error function.
  `Apfloat`
  `erfi(Apfloat x)`
  Imaginary error function.
  `Apfloat`
  `eulerE(long n, Apfloat x)`
  Euler polynomial.
  `Apfloat`
  `exp(Apfloat x)`
  Exponential function.
  `Apfloat`
  `expIntegralE(Apfloat ν, Apfloat x)`
  Exponential integral E.
  `Apfloat`
  `expIntegralEi(Apfloat x)`
  Exponential integral Ei.
  `Apfloat`
  `factorial(long n)`
  Factorial.
  `Apfloat`
  `factorial(long n, int radix)`
  Factorial.
  `Apfloat`
  `fibonacci(Apfloat ν, Apfloat x)`
  Fibonacci function.
  `Apfloat`
  `floor(Apfloat x)`
  Floor function.
  `Apfloat`
  `fmod(Apfloat x, Apfloat y)`
  Modulus.
  `Apfloat`
  `frac(Apfloat x)`
  Extract fractional part.
  `Apfloat`
  `fresnelC(Apfloat x)`
  Fresnel integral C.
  `Apfloat`
  `fresnelS(Apfloat x)`
  Fresnel integral S.
  `Apfloat`
  `gamma(Apfloat x)`
  Gamma function.
  `Apfloat`
  `gamma(Apfloat a, Apfloat x)`
  Incomplete gamma function.
  `Apfloat`
  `gamma(Apfloat a, Apfloat x0, Apfloat x1)`
  Generalized incomplete gamma function.
  `Apfloat`
  `gegenbauerC(Apfloat ν, Apfloat x)`
  Renormalized Gegenbauer function.
  `Apfloat`
  `gegenbauerC(Apfloat ν, Apfloat λ, Apfloat x)`
  Gegenbauer function.
  `Apfloat`
  `harmonicNumber(Apfloat x)`
  Harmonic number.
  `Apfloat`
  `harmonicNumber(Apfloat x, Apfloat r)`
  Generalized harmonic number.
  `Apfloat`
  `hermiteH(Apfloat ν, Apfloat x)`
  Hermite function.
  `Apfloat`
  `hypergeometric0F1(Apfloat a, Apfloat x)`
  Confluent hypergeometric function 0F1.
  `Apfloat`
  `hypergeometric0F1Regularized(Apfloat a, Apfloat x)`
  Regularized confluent hypergeometric function 0F̃1.
  `Apfloat`
  `hypergeometric1F1(Apfloat a, Apfloat b, Apfloat x)`
  Kummer confluent hypergeometric function 1F1.
  `Apfloat`
  `hypergeometric1F1Regularized(Apfloat a, Apfloat b, Apfloat x)`
  Regularized Kummer confluent hypergeometric function 1F̃1.
  `Apfloat`
  `hypergeometric2F1(Apfloat a, Apfloat b, Apfloat c, Apfloat x)`
  Hypergeometric function 2F1.
  `Apfloat`
  `hypergeometric2F1Regularized(Apfloat a, Apfloat b, Apfloat c, Apfloat x)`
  Regularized hypergeometric function 2F̃1.
  `Apfloat`
  `hypergeometricU(Apfloat a, Apfloat b, Apfloat x)`
  Tricomi's confluent hypergeometric function U.
  `Apfloat`
  `inverseErf(Apfloat x)`
  Inverse error function.
  `Apfloat`
  `inverseErfc(Apfloat x)`
  Inverse complementary error function.
  `Apfloat`
  `inverseRoot(Apfloat x, long n)`
  Inverse root.
  `Apfloat`
  `jacobiP(Apfloat ν, Apfloat a, Apfloat b, Apfloat x)`
  Jacobi function.
  `Apfloat`
  `laguerreL(Apfloat ν, Apfloat x)`
  Laguerre function.
  `Apfloat`
  `laguerreL(Apfloat ν, Apfloat λ, Apfloat x)`
  Generalized Laguerre function.
  `Apfloat`
  `legendreP(Apfloat ν, Apfloat x)`
  Legendre function.
  `Apfloat`
  `legendreP(Apfloat ν, Apfloat μ, Apfloat x)`
  Associated Legendre function of the first kind.
  `Apfloat`
  `legendreQ(Apfloat ν, Apfloat x)`
  Legendre function of the second kind.
  `Apfloat`
  `legendreQ(Apfloat ν, Apfloat μ, Apfloat x)`
  Associated Legendre function of the second kind.
  `Apfloat`
  `log(Apfloat x)`
  Natural logarithm.
  `Apfloat`
  `log(Apfloat x, Apfloat b)`
  Logarithm in specified base.
  `Apfloat`
  `logBarnesG(Apfloat x)`
  Logarithm of the Barnes G-function.
  `Apfloat`
  `logGamma(Apfloat x)`
  Logarithm of the gamma function.
  `Apfloat`
  `logIntegral(Apfloat x)`
  Logarithmic integral.
  `Apfloat`
  `logisticSigmoid(Apfloat x)`
  Logistic sigmoid.
  `Apfloat`
  `logRadix(int radix)`
  Logarithm.
  `Apfloat`
  `max(Apfloat x, Apfloat y)`
  Maximum value.
  `Apfloat`
  `min(Apfloat x, Apfloat y)`
  Minimum value.
  `Apfloat`
  `mod(Apfloat x, Apfloat y)`
  Modulus.
  `Apfloat[]`
  `modf(Apfloat x)`
  Split to integer and fractional parts.
  `Apfloat`
  `multiply(Apfloat x, Apfloat y)`
  Multiplication.
  `Apfloat`
  `multiplyAdd(Apfloat a, Apfloat b, Apfloat c, Apfloat d)`
  Fused multiply-add.
  `Apfloat`
  `multiplySubtract(Apfloat a, Apfloat b, Apfloat c, Apfloat d)`
  Fused multiply-subtract.
  `Apfloat`
  `negate(Apfloat x)`
  Negation.
  `Apfloat`
  `nextAfter(Apfloat x, Apfloat y)`
  The number adjacent to the first argument in the direction of the second argument.
  `Apfloat`
  `nextDown(Apfloat x)`
  The adjacent value closer to negative infinity.
  `Apfloat`
  `nextUp(Apfloat x)`
  The adjacent value closer to positive infinity.
  `Apfloat`
  `pi()`
  π.
  `Apfloat`
  `pi(int radix)`
  π.
  `Apfloat`
  `pochhammer(Apfloat x, Apfloat n)`
  Pochhammer symbol.
  `Apfloat`
  `polygamma(long n, Apfloat x)`
  Polygamma function.
  `Apfloat`
  `polylog(Apfloat ν, Apfloat x)`
  Polylogarithm.
  `Apfloat`
  `pow(Apfloat x, long n)`
  Integer power.
  `Apfloat`
  `pow(Apfloat x, Apfloat y)`
  Power.
  `Apfloat`
  `product(Apfloat... x)`
  Product.
  `Apfloat`
  `random()`
  Return a uniformly distributed random number `0 ≤ x < 1`.
  `Apfloat`
  `random(int radix)`
  Return a uniformly distributed random number `0 ≤ x < 1`.
  `Apfloat`
  `randomGaussian()`
  Return a normally distributed random number with mean 0 and standard deviation 1.
  `Apfloat`
  `randomGaussian(int radix)`
  Return a normally distributed random number with mean 0 and standard deviation 1.
  `Apfloat`
  `root(Apfloat x, long n)`
  Root.
  `Apfloat`
  `round(Apfloat x, RoundingMode roundingMode)`
  Deprecated.
  Use `roundToPrecision(Apfloat,RoundingMode)`.
  `Apfloat`
  `roundToInteger(Apfloat x, RoundingMode roundingMode)`
  Round to integer with specified rounding mode.
  `Apfloat`
  `roundToMultiple(Apfloat x, Apfloat y, RoundingMode roundingMode)`
  Round to multiple with specified rounding mode.
  `Apfloat`
  `roundToPlaces(Apfloat x, long places, RoundingMode roundingMode)`
  Round to specified number of places with specified rounding mode.
  `Apfloat`
  `roundToPrecision(Apfloat x, RoundingMode roundingMode)`
  Round to precision with specified rounding mode.
  `Apfloat`
  `scale(Apfloat x, long scale)`
  Move the radix point.
  `Apfloat`
  `sin(Apfloat x)`
  Sine.
  `Apfloat`
  `sinc(Apfloat x)`
  Sinc.
  `Apfloat`
  `sinh(Apfloat x)`
  Hyperbolic sine.
  `Apfloat`
  `sinhIntegral(Apfloat x)`
  Hyperbolic sine integral.
  `Apfloat`
  `sinIntegral(Apfloat x)`
  Sine integral.
  `Apfloat`
  `sqrt(Apfloat x)`
  Square root.
  `Apfloat`
  `struveH(Apfloat ν, Apfloat x)`
  Struve function 𝐇.
  `Apfloat`
  `struveL(Apfloat ν, Apfloat x)`
  Modified Struve function 𝐋.
  `Apfloat`
  `subtract(Apfloat x, Apfloat y)`
  Subtraction.
  `Apfloat`
  `sum(Apfloat... x)`
  Sum.
  `Apfloat`
  `tan(Apfloat x)`
  Tangent.
  `Apfloat`
  `tanh(Apfloat x)`
  Hyperbolic tangent.
  `Apfloat`
  `toDegrees(Apfloat x)`
  Convert radians to degrees.
  `Apfloat`
  `toRadians(Apfloat x)`
  Convert degrees to radians.
  `Apfloat`
  `truncate(Apfloat x)`
  Truncate fractional part.
  `Apfloat`
  `ulp(Apfloat x)`
  Unit in the last place.
  `Apfloat`
  `valueOf(Apfloat x)`
  Returns the value with the specified precision.
  `Apfloat`
  `w(Apfloat x)`
  Lambert W function.
  `Apfloat`
  `weberE(Apfloat ν, Apfloat x)`
  Weber function 𝐄.
  `Apfloat`
  `zeta(Apfloat s)`
  Riemann zeta function.
  `Apfloat`
  `zeta(Apfloat s, Apfloat a)`
  Hurwitz zeta function.

  ### Methods inherited from class FixedPrecisionApcomplexHelper

  `abs, acos, acosh, add, agm, airyAi, airyAiPrime, airyBi, airyBiPrime, allRoots, angerJ, arg, asin, asinh, atan, atanh, barnesG, bernoulli, bernoulli, bernoulliB, besselI, besselJ, besselK, besselY, beta, beta, beta, binomial, binomial, binomial, catalan, catalan, cbrt, chebyshevT, chebyshevU, clausenC, clausenCl, clausenS, clausenSl, conj, cos, cosh, coshIntegral, cosIntegral, dawsonF, digamma, divide, e, e, ellipticE, ellipticK, erf, erfc, erfi, euler, euler, eulerE, exp, expIntegralE, expIntegralEi, fibonacci, fresnelC, fresnelS, gamma, gamma, gamma, gegenbauerC, gegenbauerC, glaisher, glaisher, harmonicNumber, harmonicNumber, hermiteH, hypergeometric0F1, hypergeometric0F1Regularized, hypergeometric1F1, hypergeometric1F1Regularized, hypergeometric2F1, hypergeometric2F1Regularized, hypergeometricU, imag, inverseRoot, inverseRoot, jacobiP, khinchin, khinchin, laguerreL, laguerreL, legendreP, legendreP, legendreQ, legendreQ, log, log, logBarnesG, logGamma, logIntegral, logisticSigmoid, multiply, negate, norm, pochhammer, polygamma, polylog, pow, pow, precision, product, real, root, root, scale, sin, sinc, sinh, sinhIntegral, sinIntegral, sphericalHarmonicY, sqrt, struveH, struveL, subtract, sum, tan, tanh, ulp, valueOf, w, w, weberE, zeta, zeta`

  ### Methods inherited from class Object

  `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- ## Constructor Details

  - ### FixedPrecisionApfloatHelper

    public FixedPrecisionApfloatHelper(long precision) throws IllegalArgumentException
    Constructs an apfloat fixed-precison helper with the specified precision. The results of all mathematical operations are set to the specified precision.
    Parameters:
      `precision` - The precision of the results.
    Throws:
      `IllegalArgumentException` - In case the precision is invalid.

- ## Method Details

  - ### valueOf

    public Apfloat valueOf(Apfloat x)
    Returns the value with the specified precision.
    Parameters:
      `x` - The value.
    Returns:
      The value with to the specified precision.

  - ### negate

    public Apfloat negate(Apfloat x) throws ApfloatRuntimeException
    Negation.
    Parameters:
      `x` - The value to negate.
    Returns:
      `-x`.
    Throws:
      `ApfloatRuntimeException`

  - ### add

    public Apfloat add(Apfloat x, Apfloat y) throws ApfloatRuntimeException
    Addition.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      `x + y`.
    Throws:
      `ApfloatRuntimeException`

  - ### subtract

    public Apfloat subtract(Apfloat x, Apfloat y) throws ApfloatRuntimeException
    Subtraction.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      `x - y`.
    Throws:
      `ApfloatRuntimeException`

  - ### multiply

    public Apfloat multiply(Apfloat x, Apfloat y) throws ApfloatRuntimeException
    Multiplication.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      `x * y`.
    Throws:
      `ApfloatRuntimeException`

  - ### divide

    public Apfloat divide(Apfloat x, Apfloat y) throws ArithmeticException, ApfloatRuntimeException
    Division.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      `x / y`.
    Throws:
      `ArithmeticException` - If `y` is zero.
      `ApfloatRuntimeException`

  - ### pow

    public Apfloat pow(Apfloat x, Apfloat y) throws ArithmeticException, ApfloatRuntimeException
    Power.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      `xy`.
    Throws:
      `ArithmeticException` - If `x` and `y` are zero, or `x` is negative and `y` is not an integer.
      `ApfloatRuntimeException`

  - ### pow

    public Apfloat pow(Apfloat x, long n) throws ArithmeticException, ApfloatRuntimeException
    Integer power.
    Parameters:
      `x` - The first operand.
      `n` - The second operand.
    Returns:
      `xn`.
    Throws:
      `ArithmeticException` - If `x` and `n` are zero, or `x` is zero and `n` is negative.
      `ApfloatRuntimeException`

  - ### abs

    public Apfloat abs(Apfloat x) throws ApfloatRuntimeException
    Absolute value.
    Parameters:
      `x` - The operand.
    Returns:
      The absolute value of `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### acos

    public Apfloat acos(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Arc cosine.
    Parameters:
      `x` - The operand.
    Returns:
      The arc cosine of `x`.
    Throws:
      `ArithmeticException` - If the absolute value of `x` is more than one.
      `ApfloatRuntimeException`

  - ### acosh

    public Apfloat acosh(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Hyperbolic arc cosine.
    Parameters:
      `x` - The operand.
    Returns:
      The hyperbolic arc cosine of `x`.
    Throws:
      `ArithmeticException` - If the `x` is less than one.
      `ApfloatRuntimeException`

  - ### asin

    public Apfloat asin(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Arc sine.
    Parameters:
      `x` - The operand.
    Returns:
      The arc sine of `x`.
    Throws:
      `ArithmeticException` - If the absolute value of `x` is more than one.
      `ApfloatRuntimeException`

  - ### asinh

    public Apfloat asinh(Apfloat x) throws ApfloatRuntimeException
    Hyperbolic arc sine.
    Parameters:
      `x` - The operand.
    Returns:
      The hyperbolic arc sine of `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### atan

    public Apfloat atan(Apfloat x) throws ApfloatRuntimeException
    Arc tangent.
    Parameters:
      `x` - The operand.
    Returns:
      The arc tangent of `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### atanh

    public Apfloat atanh(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Hyperbolic arc tangent.
    Parameters:
      `x` - The operand.
    Returns:
      The hyperbolic arc tangent of `x`.
    Throws:
      `ArithmeticException` - If the absolute value of `x` is equal to or more than one.
      `ApfloatRuntimeException`

  - ### cbrt

    public Apfloat cbrt(Apfloat x) throws ApfloatRuntimeException
    Cube root.
    Parameters:
      `x` - The operand.
    Returns:
      The cube root of `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### cos

    public Apfloat cos(Apfloat x) throws ApfloatRuntimeException
    Cosine.
    Parameters:
      `x` - The operand.
    Returns:
      The cosine of `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### cosh

    public Apfloat cosh(Apfloat x) throws ApfloatRuntimeException
    Hyperbolic cosine.
    Parameters:
      `x` - The operand.
    Returns:
      The hyperbolic cosine of `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### exp

    public Apfloat exp(Apfloat x) throws ApfloatRuntimeException
    Exponential function.
    Parameters:
      `x` - The operand.
    Returns:
      `ex`.
    Throws:
      `ApfloatRuntimeException`

  - ### log

    public Apfloat log(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Natural logarithm.
    Parameters:
      `x` - The operand.
    Returns:
      The natural logarithm of `x`.
    Throws:
      `ArithmeticException` - If `x` is less than or equal to zero.
      `ApfloatRuntimeException`

  - ### log

    public Apfloat log(Apfloat x, Apfloat b) throws ArithmeticException, ApfloatRuntimeException
    Logarithm in specified base.
    Parameters:
      `x` - The operand.
      `b` - The base.
    Returns:
      The base-`b` logarithm of `x`.
    Throws:
      `ArithmeticException` - If `x` or `b` is less than or equal to zero.
      `ApfloatRuntimeException`
    Since:
      1.6

  - ### sin

    public Apfloat sin(Apfloat x) throws ApfloatRuntimeException
    Sine.
    Parameters:
      `x` - The operand.
    Returns:
      The sine of `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### sinh

    public Apfloat sinh(Apfloat x) throws ApfloatRuntimeException
    Hyperbolic sine.
    Parameters:
      `x` - The operand.
    Returns:
      The hyperbolic sine of `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### sqrt

    public Apfloat sqrt(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Square root.
    Parameters:
      `x` - The operand.
    Returns:
      The square root of `x`.
    Throws:
      `ArithmeticException` - If `x` is negative.
      `ApfloatRuntimeException`

  - ### tan

    public Apfloat tan(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Tangent.
    Parameters:
      `x` - The operand.
    Returns:
      The tangent of `x`.
    Throws:
      `ArithmeticException` - If `x` is π/2 + n π where n is an integer.
      `ApfloatRuntimeException`

  - ### tanh

    public Apfloat tanh(Apfloat x) throws ApfloatRuntimeException
    Hyperbolic tangent.
    Parameters:
      `x` - The operand.
    Returns:
      The hyperbolic tangent of `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### sinc

    public Apfloat sinc(Apfloat x) throws ApfloatRuntimeException
    Sinc.
    Parameters:
      `x` - The argument.
    Returns:
      sinc(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### agm

    public Apfloat agm(Apfloat a, Apfloat b) throws ApfloatRuntimeException
    Arithmetic-geometric mean.
    Parameters:
      `a` - The first operand.
      `b` - The first operand.
    Returns:
      The arithmetic-geometric mean of `a` and `b`.
    Throws:
      `ApfloatRuntimeException`

  - ### inverseRoot

    public Apfloat inverseRoot(Apfloat x, long n) throws ArithmeticException, ApfloatRuntimeException
    Inverse root.
    Parameters:
      `x` - The operand.
      `n` - Which inverse root to take.
    Returns:
      `x-1/n`.
    Throws:
      `ArithmeticException` - If `x` or `n` is zero, or `x` is negative and `n` is even.
      `ApfloatRuntimeException`

  - ### root

    public Apfloat root(Apfloat x, long n) throws ArithmeticException, ApfloatRuntimeException
    Root.
    Parameters:
      `x` - The operand.
      `n` - Which root to take.
    Returns:
      `x1/n`.
    Throws:
      `ArithmeticException` - If `n` is zero, or `x` is negative and `n` is even.
      `ApfloatRuntimeException`

  - ### scale

    public Apfloat scale(Apfloat x, long scale) throws ApfloatRuntimeException
    Move the radix point.
    Parameters:
      `x` - The operand.
      `scale` - The amount to move the radix point.
    Returns:
      `x * x.radix()scale`.
    Throws:
      `ApfloatRuntimeException`

  - ### mod

    public Apfloat mod(Apfloat x, Apfloat y) throws ApfloatRuntimeException
    Modulus.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      `x % y`.
    Throws:
      `ApfloatRuntimeException`

  - ### ceil

    public Apfloat ceil(Apfloat x) throws ApfloatRuntimeException
    Ceiling function.
    Parameters:
      `x` - The operand.
    Returns:
      The nearest integer greater than or equal to `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### floor

    public Apfloat floor(Apfloat x) throws ApfloatRuntimeException
    Floor function.
    Parameters:
      `x` - The operand.
    Returns:
      The nearest integer less than or equal to `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### truncate

    public Apfloat truncate(Apfloat x) throws ApfloatRuntimeException
    Truncate fractional part.
    Parameters:
      `x` - The operand.
    Returns:
      The nearest integer rounded towards zero from `x`.
    Throws:
      `ApfloatRuntimeException`

  - ### frac

    public Apfloat frac(Apfloat x) throws ApfloatRuntimeException
    Extract fractional part.
    Parameters:
      `x` - The operand.
    Returns:
      The fractional part of `x`.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.7.0

  - ### round

    @Deprecated public Apfloat round(Apfloat x, RoundingMode roundingMode) throws ApfloatRuntimeException
    Deprecated.
    Use `roundToPrecision(Apfloat,RoundingMode)`.
    Round with specified rounding mode.
    Parameters:
      `x` - The operand.
      `roundingMode` - The rounding mode.
    Returns:
      `x` rounded with the specified rounding mode.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.7.0

  - ### roundToPrecision

    public Apfloat roundToPrecision(Apfloat x, RoundingMode roundingMode) throws ApfloatRuntimeException
    Round to precision with specified rounding mode.
    Parameters:
      `x` - The operand.
      `roundingMode` - The rounding mode.
    Returns:
      `x` rounded to the precision of this helper with the specified rounding mode.
    Throws:
      `ArithmeticException` - If rounding is necessary (result is not exact) and rounding mode is `RoundingMode.UNNECESSARY`.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### roundToInteger

    public Apfloat roundToInteger(Apfloat x, RoundingMode roundingMode) throws ApfloatRuntimeException, ArithmeticException
    Round to integer with specified rounding mode.
    Parameters:
      `x` - The operand.
      `roundingMode` - The rounding mode.
    Returns:
      `x` rounded to integer with the specified rounding mode.
    Throws:
      `ArithmeticException` - If rounding is necessary (result is not exact) and rounding mode is `RoundingMode.UNNECESSARY`.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### roundToPlaces

    public Apfloat roundToPlaces(Apfloat x, long places, RoundingMode roundingMode) throws ApfloatRuntimeException, ArithmeticException
    Round to specified number of places with specified rounding mode.
    Parameters:
      `x` - The operand.
      `places` - The number of places.
      `roundingMode` - The rounding mode.
    Returns:
      `x` rounded to the specified number of places with the specified rounding mode.
    Throws:
      `ArithmeticException` - If rounding is necessary (result is not exact) and rounding mode is `RoundingMode.UNNECESSARY`.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### roundToMultiple

    public Apfloat roundToMultiple(Apfloat x, Apfloat y, RoundingMode roundingMode) throws ApfloatRuntimeException, ArithmeticException
    Round to multiple with specified rounding mode.
    Parameters:
      `x` - The number to round.
      `y` - The integer multiple to round to.
      `roundingMode` - The rounding mode.
    Returns:
      `x` rounded to the nearest multiple of `y` with the specified rounding mode.
    Throws:
      `ArithmeticException` - If rounding is necessary (result is not exact) and rounding mode is `RoundingMode.UNNECESSARY`.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### w

    public Apfloat w(Apfloat x) throws ApfloatRuntimeException
    Lambert W function.
    Parameters:
      `x` - The operand.
    Returns:
      `W0(x)`.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.8.0

  - ### toDegrees

    public Apfloat toDegrees(Apfloat x) throws ApfloatRuntimeException
    Convert radians to degrees.
    Parameters:
      `x` - The angle in radians.
    Returns:
      `x` converted to degrees.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.8.0

  - ### toRadians

    public Apfloat toRadians(Apfloat x) throws ApfloatRuntimeException
    Convert degrees to radians.
    Parameters:
      `x` - The angle in degrees.
    Returns:
      `x` converted to radians.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.8.0

  - ### atan2

    public Apfloat atan2(Apfloat x, Apfloat y) throws ArithmeticException, ApfloatRuntimeException
    Angle of point.
    Parameters:
      `x` - The operand.
      `y` - The operand.
    Returns:
      The angle of the point `(y, x)`.
    Throws:
      `ArithmeticException` - If `x` and `y` are zero.
      `ApfloatRuntimeException`

  - ### copySign

    public Apfloat copySign(Apfloat x, Apfloat y) throws ApfloatRuntimeException
    Copies the sign from one number to another.
    Parameters:
      `x` - The number to copy the sign to.
      `y` - The number to copy the sign from.
    Returns:
      `x` with the sign of `y`.
    Throws:
      `ApfloatRuntimeException`

  - ### fmod

    public Apfloat fmod(Apfloat x, Apfloat y) throws ApfloatRuntimeException
    Modulus.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      `x % y`.
    Throws:
      `ApfloatRuntimeException`

  - ### modf

    public Apfloat[] modf(Apfloat x) throws ApfloatRuntimeException
    Split to integer and fractional parts.
    Parameters:
      `x` - The operand.
    Returns:
      An array of two numbers `[i, f]` where `i` is `floor(x)` and `f` is `x - floor(x)`.
    Throws:
      `ApfloatRuntimeException`

  - ### factorial

    public Apfloat factorial(long n) throws ApfloatRuntimeException
    Factorial.
    Parameters:
      `n` - The operand.
    Returns:
      `n!`.
    Throws:
      `ApfloatRuntimeException`

  - ### factorial

    public Apfloat factorial(long n, int radix) throws ApfloatRuntimeException
    Factorial.
    Parameters:
      `n` - The operand.
      `radix` - The radix of the result.
    Returns:
      `n!`.
    Throws:
      `ApfloatRuntimeException`

  - ### doubleFactorial

    public Apfloat doubleFactorial(long n) throws ApfloatRuntimeException
    Double factorial.
    Parameters:
      `n` - The operand.
    Returns:
      `n!!`.
    Throws:
      `ArithmeticException` - If `n` is negative and even.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### doubleFactorial

    public Apfloat doubleFactorial(long n, int radix) throws ApfloatRuntimeException
    Double factorial.
    Parameters:
      `n` - The operand.
      `radix` - The radix of the result.
    Returns:
      `n!!`.
    Throws:
      `ArithmeticException` - If `n` is negative and even.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### pi

    public Apfloat pi() throws ApfloatRuntimeException
    π.
    Returns:
      `π`.
    Throws:
      `ApfloatRuntimeException`

  - ### pi

    public Apfloat pi(int radix) throws NumberFormatException, ApfloatRuntimeException
    π.
    Parameters:
      `radix` - The radix of the result.
    Returns:
      `π`.
    Throws:
      `NumberFormatException` - If the radix is invalid.
      `ApfloatRuntimeException`

  - ### logRadix

    public Apfloat logRadix(int radix) throws NumberFormatException, ApfloatRuntimeException
    Logarithm.
    Parameters:
      `radix` - The radix of the result.
    Returns:
      `log(radix)`.
    Throws:
      `NumberFormatException` - If the radix is invalid.
      `ApfloatRuntimeException`

  - ### multiplyAdd

    public Apfloat multiplyAdd(Apfloat a, Apfloat b, Apfloat c, Apfloat d) throws ApfloatRuntimeException
    Fused multiply-add.
    Parameters:
      `a` - The first operand.
      `b` - The second operand.
      `c` - The third operand.
      `d` - The fourth operand.
    Returns:
      `a * b + c * d`.
    Throws:
      `ApfloatRuntimeException`

  - ### multiplySubtract

    public Apfloat multiplySubtract(Apfloat a, Apfloat b, Apfloat c, Apfloat d) throws ApfloatRuntimeException
    Fused multiply-subtract.
    Parameters:
      `a` - The first operand.
      `b` - The second operand.
      `c` - The third operand.
      `d` - The fourth operand.
    Returns:
      `a * b - c * d`.
    Throws:
      `ApfloatRuntimeException`

  - ### product

    public Apfloat product(Apfloat... x) throws ApfloatRuntimeException
    Product.
    Parameters:
      `x` - The operand(s).
    Returns:
      The product of the operands.
    Throws:
      `ApfloatRuntimeException`

  - ### sum

    public Apfloat sum(Apfloat... x) throws ApfloatRuntimeException
    Sum.
    Parameters:
      `x` - The operand(s).
    Returns:
      The sum of the operands.
    Throws:
      `ApfloatRuntimeException`

  - ### gamma

    public Apfloat gamma(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Gamma function.
    Parameters:
      `x` - The operand.
    Returns:
      `Γ(x)`.
    Throws:
      `ArithmeticException` - If `x` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.9.0

  - ### gamma

    public Apfloat gamma(Apfloat a, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Incomplete gamma function.
    Parameters:
      `a` - The first operand.
      `x` - The second operand.
    Returns:
      `Γ(a, x)`.
    Throws:
      `ArithmeticException` - If `a` is not a positive integer and `x` is nonpositive.
      `ApfloatRuntimeException`
    Since:
      1.10.0

  - ### gamma

    public Apfloat gamma(Apfloat a, Apfloat x0, Apfloat x1) throws ArithmeticException, ApfloatRuntimeException
    Generalized incomplete gamma function.
    Parameters:
      `a` - The first operand.
      `x0` - The second operand.
      `x1` - The third operand.
    Returns:
      `Γ(a, x0) - Γ(a, x1)`.
    Throws:
      `ArithmeticException` - If `a` is not a positive integer and either `x0` or `x1` is nonpositive.
      `ApfloatRuntimeException`
    Since:
      1.10.0

  - ### logGamma

    public Apfloat logGamma(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Logarithm of the gamma function.
    Parameters:
      `x` - The argument.
    Returns:
      `logΓ(x)`
    Throws:
      `ArithmeticException` - If `x` is nonpositive.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### digamma

    public Apfloat digamma(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Digamma function.
    Parameters:
      `x` - The argument.
    Returns:
      `ψ(x)`
    Throws:
      `ArithmeticException` - If `x` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### polygamma

    public Apfloat polygamma(long n, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Polygamma function.
    Parameters:
      `n` - The order.
      `x` - The argument.
    Returns:
      `ψ(n)(x)`
    Throws:
      `ArithmeticException` - If `n ≥ -1` and `x` is a nonpositive integer, or `n ≤ -1` and `x` is negative.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### barnesG

    public Apfloat barnesG(Apfloat x) throws ApfloatRuntimeException
    Barnes G-function.
    Parameters:
      `x` - The argument.
    Returns:
      G(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.16.0

  - ### logBarnesG

    public Apfloat logBarnesG(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Logarithm of the Barnes G-function.
    Parameters:
      `x` - The argument.
    Returns:
      logG(x)
    Throws:
      `ArithmeticException` - If `x` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.16.0

  - ### beta

    public Apfloat beta(Apfloat a, Apfloat b) throws ArithmeticException, ApfloatRuntimeException
    Beta function.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
    Returns:
      B(a, b)
    Throws:
      `ArithmeticException` - If `a` or `b` is a nonpositive integer but `a + b` is not. Also if both `a` and `b` are nonpositive integers.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### beta

    public Apfloat beta(Apfloat x, Apfloat a, Apfloat b) throws ArithmeticException, ApfloatRuntimeException
    Incomplete beta function.
    Parameters:
      `x` - The first argument.
      `a` - The second argument.
      `b` - The third argument.
    Returns:
      Bx(a, b)
    Throws:
      `ArithmeticException` - If `a` is a nonpositive integer or `x` is zero and `a` is nonpositive or `x` is negative and `a` is not an integer. Also if `x` > 1 and the result is not a polynomial.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### beta

    public Apfloat beta(Apfloat x1, Apfloat x2, Apfloat a, Apfloat b) throws ArithmeticException, ApfloatRuntimeException
    Generalized incomplete beta function.
    Parameters:
      `x1` - The first argument.
      `x2` - The second argument.
      `a` - The third argument.
      `b` - The fourth argument.
    Returns:
      B(x1, x2)(a, b)
    Throws:
      `ArithmeticException` - If `a` is a nonpositive integer or `x1` or `x2` is zero and `a` is nonpositive or `x1` or `x2` is negative and `a` is not an integer. Also if `x1` > 1 or `x2` > 1 and the result is not a polynomial.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### pochhammer

    public Apfloat pochhammer(Apfloat x, Apfloat n) throws ArithmeticException, ApfloatRuntimeException
    Pochhammer symbol.
    Parameters:
      `x` - The first argument.
      `n` - The second argument.
    Returns:
      `(x)n`
    Throws:
      `ArithmeticException` - If `x + n` is a nonpositive integer but `x` is not.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### binomial

    public Apfloat binomial(Apfloat n, Apfloat k) throws ArithmeticException, ApfloatRuntimeException
    Binomial coefficient.
    Parameters:
      `n` - The argument.
      `k` - The argument.
    Returns:
      The binomial coefficient.
    Throws:
      `ArithmeticException` - If `n`, `k` or `n - k` is a nonpositive integer.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### zeta

    public Apfloat zeta(Apfloat s) throws ArithmeticException, ApfloatRuntimeException
    Riemann zeta function.
    Parameters:
      `s` - The argument.
    Returns:
      `ζ(s)`
    Throws:
      `ArithmeticException` - If `s` is `1`.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### zeta

    public Apfloat zeta(Apfloat s, Apfloat a) throws ArithmeticException, ApfloatRuntimeException
    Hurwitz zeta function.
    Parameters:
      `s` - The first argument.
      `a` - The second argument.
    Returns:
      `ζ(s, a)`
    Throws:
      `ArithmeticException` - If `s` is `1` or if `a` is a nonpositive integer or if `s` is not an integer and `a` is nonpositive.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### hypergeometric0F1

    public Apfloat hypergeometric0F1(Apfloat a, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Confluent hypergeometric function 0F1.
    Parameters:
      `a` - The first argument.
      `x` - The second argument.
    Returns:
      0F1(; a; x)
    Throws:
      `ArithmeticException` - If the function value is not finite.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### hypergeometric0F1Regularized

    public Apfloat hypergeometric0F1Regularized(Apfloat a, Apfloat x) throws ApfloatRuntimeException
    Regularized confluent hypergeometric function 0F̃1.
    Parameters:
      `a` - The first argument.
      `x` - The second argument.
    Returns:
      0F̃1(; a; x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### hypergeometric1F1

    public Apfloat hypergeometric1F1(Apfloat a, Apfloat b, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Kummer confluent hypergeometric function 1F1.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `x` - The third argument.
    Returns:
      1F1(a; b; x)
    Throws:
      `ArithmeticException` - If the function value is not finite.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### hypergeometric1F1Regularized

    public Apfloat hypergeometric1F1Regularized(Apfloat a, Apfloat b, Apfloat x) throws ApfloatRuntimeException
    Regularized Kummer confluent hypergeometric function 1F̃1.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `x` - The third argument.
    Returns:
      1F̃1(a; b; x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### hypergeometric2F1

    public Apfloat hypergeometric2F1(Apfloat a, Apfloat b, Apfloat c, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Hypergeometric function 2F1.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `c` - The third argument.
      `x` - The fourth argument.
    Returns:
      2F1(a, b; c; x)
    Throws:
      `ArithmeticException` - If the function value is not finite or real.
      `ApfloatRuntimeException`
    Since:
      1.11.0

  - ### hypergeometric2F1Regularized

    public Apfloat hypergeometric2F1Regularized(Apfloat a, Apfloat b, Apfloat c, Apfloat x) throws ApfloatRuntimeException
    Regularized hypergeometric function 2F̃1.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `c` - The third argument.
      `x` - The fourth argument.
    Returns:
      2F̃1(a, b; c; x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### hypergeometricU

    public Apfloat hypergeometricU(Apfloat a, Apfloat b, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Tricomi's confluent hypergeometric function U.
    Parameters:
      `a` - The first argument.
      `b` - The second argument.
      `x` - The third argument.
    Returns:
      U(a, b, x)
    Throws:
      `ArithmeticException` - If the result would be complex or not finite.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### erf

    public Apfloat erf(Apfloat x) throws ApfloatRuntimeException
    Error function.
    Parameters:
      `x` - The argument.
    Returns:
      erf(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### erfc

    public Apfloat erfc(Apfloat x) throws ApfloatRuntimeException
    Complementary error function.
    Parameters:
      `x` - The argument.
    Returns:
      erfc(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### erfi

    public Apfloat erfi(Apfloat x) throws ApfloatRuntimeException
    Imaginary error function.
    Parameters:
      `x` - The argument.
    Returns:
      erfi(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### inverseErf

    public Apfloat inverseErf(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Inverse error function.
    Parameters:
      `x` - The argument.
    Returns:
      erf−1(x)
    Throws:
      `ArithmeticException` - If `|x|` is ≥ 1.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### inverseErfc

    public Apfloat inverseErfc(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Inverse complementary error function.
    Parameters:
      `x` - The argument.
    Returns:
      erfc−1(x)
    Throws:
      `ArithmeticException` - If `x` is ≤ 0 or ≥ 2.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### dawsonF

    public Apfloat dawsonF(Apfloat x) throws ApfloatRuntimeException
    Dawson's integral F.

    Parameters:
      `x` - The argument.
    Returns:
      F(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.16.0

  - ### fresnelS

    public Apfloat fresnelS(Apfloat x) throws ApfloatRuntimeException
    Fresnel integral S.
    Parameters:
      `x` - The argument.
    Returns:
      S(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### fresnelC

    public Apfloat fresnelC(Apfloat x) throws ApfloatRuntimeException
    Fresnel integral C.
    Parameters:
      `x` - The argument.
    Returns:
      C(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### expIntegralE

    public Apfloat expIntegralE(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Exponential integral E.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Eν(x)
    Throws:
      `ArithmeticException` - If `ν` is < 0 and `x` is zero or `ν` is nonzero and `x` is negative.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### expIntegralEi

    public Apfloat expIntegralEi(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Exponential integral Ei.
    Parameters:
      `x` - The argument.
    Returns:
      Ei(x)
    Throws:
      `ArithmeticException` - If `x` is zero.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### logIntegral

    public Apfloat logIntegral(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Logarithmic integral.
    Parameters:
      `x` - The argument.
    Returns:
      li(x)
    Throws:
      `ArithmeticException` - If `x` is nonpositive or 1.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### sinIntegral

    public Apfloat sinIntegral(Apfloat x) throws ApfloatRuntimeException
    Sine integral.
    Parameters:
      `x` - The argument.
    Returns:
      Si(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### cosIntegral

    public Apfloat cosIntegral(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Cosine integral.
    Parameters:
      `x` - The argument.
    Returns:
      Ci(x)
    Throws:
      `ArithmeticException` - If `x` is nonpositive.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### sinhIntegral

    public Apfloat sinhIntegral(Apfloat x) throws ApfloatRuntimeException
    Hyperbolic sine integral.
    Parameters:
      `x` - The argument.
    Returns:
      Shi(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### coshIntegral

    public Apfloat coshIntegral(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Hyperbolic cosine integral.
    Parameters:
      `x` - The argument.
    Returns:
      Chi(x)
    Throws:
      `ArithmeticException` - If `x` is nonpositive.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### airyAi

    public Apfloat airyAi(Apfloat x) throws ApfloatRuntimeException
    Airy function Ai.
    Parameters:
      `x` - The argument.
    Returns:
      Ai(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### airyAiPrime

    public Apfloat airyAiPrime(Apfloat x) throws ApfloatRuntimeException
    Derivative of the Airy function Ai.
    Parameters:
      `x` - The argument.
    Returns:
      Ai′(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### airyBi

    public Apfloat airyBi(Apfloat x) throws ApfloatRuntimeException
    Airy function Bi.
    Parameters:
      `x` - The argument.
    Returns:
      Bi(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### airyBiPrime

    public Apfloat airyBiPrime(Apfloat x) throws ApfloatRuntimeException
    Derivative of the Airy function Bi.
    Parameters:
      `x` - The argument.
    Returns:
      Bi′(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### besselJ

    public Apfloat besselJ(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Bessel function of the first kind.
    Parameters:
      `ν` - The order.
      `x` - The argument.
    Returns:
      Jν(x)
    Throws:
      `ArithmeticException` - If `ν` is < 0 and `ν` is not an integer and `x` is zero. Also if `ν` is not an integer and `x` is < 0.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### besselI

    public Apfloat besselI(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Modified Bessel function of the first kind.
    Parameters:
      `ν` - The order.
      `x` - The argument.
    Returns:
      Iν(x)
    Throws:
      `ArithmeticException` - If `ν` is < 0 and `ν` is not an integer and `x` is zero. Also if `ν` is not an integer and `x` is < 0.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### besselY

    public Apfloat besselY(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Bessel function of the second kind.
    Parameters:
      `ν` - The order.
      `x` - The argument.
    Returns:
      Yν(x)
    Throws:
      `ArithmeticException` - If `x` is ≤ 0.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### besselK

    public Apfloat besselK(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Modified Bessel function of the second kind.
    Parameters:
      `ν` - The order.
      `x` - The argument.
    Returns:
      Kν(x)
    Throws:
      `ArithmeticException` - If `x` is ≤ 0.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### struveH

    public Apfloat struveH(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Struve function 𝐇.

    Parameters:
      `ν` - The order.
      `x` - The argument.
    Returns:
      𝐇ν(x)
    Throws:
      `ArithmeticException` - If `x` is zero and `ν` is ≤ -1.
      `ApfloatRuntimeException`
    Since:
      1.15.0

  - ### struveL

    public Apfloat struveL(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Modified Struve function 𝐋.

    Parameters:
      `ν` - The order.
      `x` - The argument.
    Returns:
      𝐋ν(x)
    Throws:
      `ArithmeticException` - If `x` is zero and `ν` is ≤ -1.
      `ApfloatRuntimeException`
    Since:
      1.15.0

  - ### angerJ

    public Apfloat angerJ(Apfloat ν, Apfloat x) throws ApfloatRuntimeException
    Anger function 𝐉.

    Parameters:
      `ν` - The order.
      `x` - The argument.
    Returns:
      𝐉ν(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.15.0

  - ### weberE

    public Apfloat weberE(Apfloat ν, Apfloat x) throws ApfloatRuntimeException
    Weber function 𝐄.

    Parameters:
      `ν` - The order.
      `x` - The argument.
    Returns:
      𝐄ν(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.15.0

  - ### ellipticK

    public Apfloat ellipticK(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Complete elliptic integral of the first kind.
    Parameters:
      `x` - The argument.
    Returns:
      K(x)
    Throws:
      `ArithmeticException` - If `x` is ≥ 1.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### ellipticE

    public Apfloat ellipticE(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Complete elliptic integral of the second kind.
    Parameters:
      `x` - The argument.
    Returns:
      E(x)
    Throws:
      `ArithmeticException` - If `x` is > 1.
      `ApfloatRuntimeException`
    Since:
      1.13.0

  - ### hermiteH

    public Apfloat hermiteH(Apfloat ν, Apfloat x) throws ApfloatRuntimeException
    Hermite function.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Hν(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### laguerreL

    public Apfloat laguerreL(Apfloat ν, Apfloat x) throws ApfloatRuntimeException
    Laguerre function.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Lν(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### laguerreL

    public Apfloat laguerreL(Apfloat ν, Apfloat λ, Apfloat x) throws ApfloatRuntimeException
    Generalized Laguerre function.
    Parameters:
      `ν` - The first argument.
      `λ` - The second argument.
      `x` - The third argument.
    Returns:
      Lνλ(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### legendreP

    public Apfloat legendreP(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Legendre function.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Pν(x)
    Throws:
      `ArithmeticException` - If `ν` is not an integer and `x` ≤ -1.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### legendreP

    public Apfloat legendreP(Apfloat ν, Apfloat μ, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Associated Legendre function of the first kind.
    Parameters:
      `ν` - The first argument.
      `μ` - The second argument.
      `x` - The third argument.
    Returns:
      Pνμ(x)
    Throws:
      `ArithmeticException` - If `x` is ≤ -1 or ≥ 1 and `ν` or `μ` is not an integer or `μ` is not even or `μ` is not positive and `-μ` ≤ `ν` < `μ`.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### legendreQ

    public Apfloat legendreQ(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Legendre function of the second kind.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Qν(x)
    Throws:
      `ArithmeticException` - If `x` is ≥ 1 or ≤ -1.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### legendreQ

    public Apfloat legendreQ(Apfloat ν, Apfloat μ, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Associated Legendre function of the second kind.
    Parameters:
      `ν` - The first argument.
      `μ` - The second argument.
      `x` - The third argument.
    Returns:
      Qνμ(x)
    Throws:
      `ArithmeticException` - If `x` is ≥ 1 or ≤ -1.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### chebyshevT

    public Apfloat chebyshevT(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Chebyshev function of the first kind.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Tν(x)
    Throws:
      `ArithmeticException` - If `x` is < -1 and `ν` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### chebyshevU

    public Apfloat chebyshevU(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Chebyshev function of the second kind.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Uν(x)
    Throws:
      `ArithmeticException` - If `x` is ≤ -1 and `ν` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### gegenbauerC

    public Apfloat gegenbauerC(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Renormalized Gegenbauer function.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Cν(0)(x)
    Throws:
      `ArithmeticException` - If `ν` is zero. Also if `x` is < -1 and `ν` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### gegenbauerC

    public Apfloat gegenbauerC(Apfloat ν, Apfloat λ, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Gegenbauer function.
    Parameters:
      `ν` - The first argument.
      `λ` - The second argument.
      `x` - The third argument.
    Returns:
      Cνλ(x)
    Throws:
      `ArithmeticException` - If `x` is < -1 and `ν` is not an integer. Also if `x` is -1 and `λ` is > 1/2. Also if `x` is -1 and `λ` is 1/2 and `ν` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### jacobiP

    public Apfloat jacobiP(Apfloat ν, Apfloat a, Apfloat b, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Jacobi function.
    Parameters:
      `ν` - The first argument.
      `a` - The second argument.
      `b` - The third argument.
      `x` - The fourth argument.
    Returns:
      Pν(a,b)(x)
    Throws:
      `ArithmeticException` - If `ν` is not a positive integer and either `x` is -1 and `b` is > 0 or `x` is < -1. Also if `ν + a` is a negative integer and `ν` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### fibonacci

    public Apfloat fibonacci(Apfloat ν, Apfloat x) throws ApfloatRuntimeException
    Fibonacci function.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Fν(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### eulerE

    public Apfloat eulerE(long n, Apfloat x) throws IllegalArgumentException, ApfloatRuntimeException
    Euler polynomial.
    Parameters:
      `n` - The first argument.
      `x` - The second argument.
    Returns:
      En(x)
    Throws:
      `IllegalArgumentException` - If `n` < 0.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### bernoulliB

    public Apfloat bernoulliB(long n, Apfloat x) throws IllegalArgumentException, ApfloatRuntimeException
    Bernoulli polynomial.
    Parameters:
      `n` - The first argument.
      `x` - The second argument.
    Returns:
      Bn(x)
    Throws:
      `IllegalArgumentException` - If `n` < 0.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### harmonicNumber

    public Apfloat harmonicNumber(Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Harmonic number.
    Parameters:
      `x` - The argument.
    Returns:
      Hx
    Throws:
      `ArithmeticException` - If `x` is a negative integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### harmonicNumber

    public Apfloat harmonicNumber(Apfloat x, Apfloat r) throws ArithmeticException, ApfloatRuntimeException
    Generalized harmonic number.
    Parameters:
      `x` - The first argument.
      `r` - The second argument.
    Returns:
      Hx(r)
    Throws:
      `ArithmeticException` - If `x` is a negative integer, unless `r` is a nonpositive integer. Also if `x` is < -1 and `r` is not an integer.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### polylog

    public Apfloat polylog(Apfloat ν, Apfloat x) throws ArithmeticException, ApfloatRuntimeException
    Polylogarithm.
    Parameters:
      `ν` - The first argument.
      `x` - The second argument.
    Returns:
      Liν(x)
    Throws:
      `ArithmeticException` - If `ν` is ≤ 1 and `x` is 1 or if `x` is > 1.
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### clausenCl

    public Apfloat clausenCl(long n, Apfloat θ) throws ArithmeticException, ApfloatRuntimeException
    Clausen function Cl.

    Parameters:
      `n` - The order.
      `θ` - The argument.
    Returns:
      Cln(θ)
    Throws:
      `ArithmeticException` - If `n` is ≤ 1 and `θ` is 0.
      `ApfloatRuntimeException`
    Since:
      1.16.0

  - ### clausenSl

    public Apfloat clausenSl(long n, Apfloat θ) throws ArithmeticException, ApfloatRuntimeException
    Clausen function Sl.

    Parameters:
      `n` - The order.
      `θ` - The argument.
    Returns:
      Sln(θ)
    Throws:
      `ArithmeticException` - If `n` is ≤ 1 and `θ` is 0.
      `ApfloatRuntimeException`
    Since:
      1.16.0

  - ### clausenS

    public Apfloat clausenS(Apfloat s, Apfloat θ) throws ArithmeticException, ApfloatRuntimeException
    Clausen function S.

    Parameters:
      `s` - The order.
      `θ` - The argument.
    Returns:
      Ss(θ)
    Throws:
      `ArithmeticException` - If `s` is ≤ 1 and `θ` is 0.
      `ApfloatRuntimeException`
    Since:
      1.16.0

  - ### clausenC

    public Apfloat clausenC(Apfloat s, Apfloat θ) throws ArithmeticException, ApfloatRuntimeException
    Clausen function C.

    Parameters:
      `s` - The order.
      `θ` - The argument.
    Returns:
      Cs(θ)
    Throws:
      `ArithmeticException` - If `s` is ≤ 1 and `θ` is 0.
      `ApfloatRuntimeException`
    Since:
      1.16.0

  - ### logisticSigmoid

    public Apfloat logisticSigmoid(Apfloat x) throws ApfloatRuntimeException
    Logistic sigmoid.
    Parameters:
      `x` - The argument.
    Returns:
      σ(x)
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.14.0

  - ### random

    public Apfloat random() throws ApfloatRuntimeException
    Return a uniformly distributed random number `0 ≤ x < 1`.
    Returns:
      A random number.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.9.0

  - ### random

    public Apfloat random(int radix) throws NumberFormatException, ApfloatRuntimeException
    Return a uniformly distributed random number `0 ≤ x < 1`.
    Parameters:
      `radix` - The radix of the number.
    Returns:
      A random number.
    Throws:
      `NumberFormatException` - If the radix is invalid.
      `ApfloatRuntimeException`
    Since:
      1.9.0

  - ### randomGaussian

    public Apfloat randomGaussian() throws ApfloatRuntimeException
    Return a normally distributed random number with mean 0 and standard deviation 1.
    Returns:
      A random number.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.9.0

  - ### randomGaussian

    public Apfloat randomGaussian(int radix) throws NumberFormatException, ApfloatRuntimeException
    Return a normally distributed random number with mean 0 and standard deviation 1.
    Parameters:
      `radix` - The radix of the number.
    Returns:
      A random number.
    Throws:
      `NumberFormatException` - If the radix is invalid.
      `ApfloatRuntimeException`
    Since:
      1.9.0

  - ### continuedFraction

    public Apfloat[] continuedFraction(Apfloat x, int n) throws ApfloatRuntimeException
    Continued fraction.
    Parameters:
      `x` - The value.
      `n` - Maximum number of terms.
    Returns:
      The continued fraction.
    Throws:
      `IllegalArgumentException` - If `n` is less than one.
      `ApfloatRuntimeException`
    Since:
      1.12.0

  - ### convergents

    public Apfloat[] convergents(Apfloat x, int n) throws ApfloatRuntimeException
    Convergents.
    Parameters:
      `x` - The value.
      `n` - Maximum number of convergents.
    Returns:
      The convergents.
    Throws:
      `IllegalArgumentException` - If `n` is less than one.
      `ApfloatRuntimeException`
    Since:
      1.12.0

  - ### max

    public Apfloat max(Apfloat x, Apfloat y) throws ApfloatRuntimeException
    Maximum value.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      The maximum of `x` and `y`.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.9.0

  - ### min

    public Apfloat min(Apfloat x, Apfloat y) throws ApfloatRuntimeException
    Minimum value.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      The minimum of `x` and `y`.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.9.0

  - ### nextAfter

    public Apfloat nextAfter(Apfloat x, Apfloat y) throws ApfloatRuntimeException
    The number adjacent to the first argument in the direction of the second argument.
    Parameters:
      `x` - The first operand.
      `y` - The second operand.
    Returns:
      The number adjacent to the first argument in the direction of the second argument.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.10.0

  - ### nextDown

    public Apfloat nextDown(Apfloat x) throws ApfloatRuntimeException
    The adjacent value closer to negative infinity.
    Parameters:
      `x` - The operand.
    Returns:
      The adjacent value closer to negative infinity.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.10.0

  - ### nextUp

    public Apfloat nextUp(Apfloat x) throws ApfloatRuntimeException
    The adjacent value closer to positive infinity.
    Parameters:
      `x` - The operand.
    Returns:
      The adjacent value closer to positive infinity.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.10.0

  - ### ulp

    public Apfloat ulp(Apfloat x) throws ApfloatRuntimeException
    Unit in the last place.
    Parameters:
      `x` - The operand.
    Returns:
      The unit in the last place.
    Throws:
      `ApfloatRuntimeException`
    Since:
      1.10.0