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:

1.14.0

Constructor Summary

Constructors
Constructor Description

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

Method Summary

All Methods Instance Methods Concrete Methods Deprecated Methods
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`	`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`	`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.
`private Apfloat`	`checkSmallLinear(Apfloat x)`
`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`	`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`	`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, java.math.RoundingMode roundingMode)`	Deprecated. Use `roundToPrecision(Apfloat,RoundingMode)`.
`Apfloat`	`roundToInteger(Apfloat x, java.math.RoundingMode roundingMode)`	Round to integer with specified rounding mode.
`Apfloat`	`roundToMultiple(Apfloat x, Apfloat y, java.math.RoundingMode roundingMode)`	Round to multiple with specified rounding mode.
`Apfloat`	`roundToPlaces(Apfloat x, long places, java.math.RoundingMode roundingMode)`	Round to specified number of places with specified rounding mode.
`Apfloat`	`roundToPrecision(Apfloat x, java.math.RoundingMode roundingMode)`	Round to precision with specified rounding mode.
`Apfloat`	`scale(Apfloat x, long scale)`	Move the radix point.
`private Apfloat`	`setPrecision(Apfloat x)`
`private Apfloat[]`	`setPrecision(Apfloat[] x)`
`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`	`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`	`zeta(Apfloat s)`	Riemann zeta function.
`Apfloat`	`zeta(Apfloat s, Apfloat a)`	Hurwitz zeta function.

Methods inherited from class org.apfloat.FixedPrecisionApcomplexHelper
abs, acos, acosh, add, agm, airyAi, airyAiPrime, airyBi, airyBiPrime, allRoots, arg, asin, asinh, atan, atanh, bernoulli, bernoulli, bernoulliB, besselI, besselJ, besselK, besselY, beta, beta, beta, binomial, binomial, binomial, catalan, catalan, cbrt, chebyshevT, chebyshevU, conj, cos, cosh, coshIntegral, cosIntegral, 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, logGamma, logIntegral, logisticSigmoid, multiply, negate, norm, pochhammer, polygamma, polylog, pow, pow, precision, product, real, root, root, scale, setErfPrecision, setExponentialPrecision, setGammaPrecision, setLogarithmicPrecision, setTrigonometricPrecision, setZetaPrecision, sin, sinc, sinh, sinhIntegral, sinIntegral, sphericalHarmonicY, sqrt, subtract, sum, tan, tanh, ulp, valueOf, w, w, zeta, zeta

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

- Constructor Detail
  - FixedPrecisionApfloatHelper
```
public FixedPrecisionApfloatHelper(long precision)
                            throws java.lang.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:
    
    java.lang.IllegalArgumentException - In case the precision is invalid.
- Method Detail
  - valueOf
```
public Apfloat valueOf(Apfloat x)
```
    Returns the value with the specified precision.
    
    Overrides:
    
    valueOf in class FixedPrecisionApcomplexHelper
    
    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 java.lang.ArithmeticException,
                      ApfloatRuntimeException
```
    Division.
    
    Parameters:
    
    x - The first operand.
    
    y - The second operand.
    
    Returns:
    
    x / y.
    
    Throws:
    
    java.lang.ArithmeticException - If y is zero.
    
    ApfloatRuntimeException
  - pow
```
public Apfloat pow(Apfloat x,
                   Apfloat y)
            throws java.lang.ArithmeticException,
                   ApfloatRuntimeException
```
    Power.
    
    Parameters:
    
    x - The first operand.
    
    y - The second operand.
    
    Returns:
    
    x^y.
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                   ApfloatRuntimeException
```
    Integer power.
    
    Parameters:
    
    x - The first operand.
    
    n - The second operand.
    
    Returns:
    
    xⁿ.
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                    ApfloatRuntimeException
```
    Arc cosine.
    
    Parameters:
    
    x - The operand.
    
    Returns:
    
    The arc cosine of x.
    
    Throws:
    
    java.lang.ArithmeticException - If the absolute value of x is more than one.
    
    ApfloatRuntimeException
  - acosh
```
public Apfloat acosh(Apfloat x)
              throws java.lang.ArithmeticException,
                     ApfloatRuntimeException
```
    Hyperbolic arc cosine.
    
    Parameters:
    
    x - The operand.
    
    Returns:
    
    The hyperbolic arc cosine of x.
    
    Throws:
    
    java.lang.ArithmeticException - If the x is less than one.
    
    ApfloatRuntimeException
  - asin
```
public Apfloat asin(Apfloat x)
             throws java.lang.ArithmeticException,
                    ApfloatRuntimeException
```
    Arc sine.
    
    Parameters:
    
    x - The operand.
    
    Returns:
    
    The arc sine of x.
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                     ApfloatRuntimeException
```
    Hyperbolic arc tangent.
    
    Parameters:
    
    x - The operand.
    
    Returns:
    
    The hyperbolic arc tangent of x.
    
    Throws:
    
    java.lang.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:
    
    e^x.
    
    Throws:
    
    ApfloatRuntimeException
  - log
```
public Apfloat log(Apfloat x)
            throws java.lang.ArithmeticException,
                   ApfloatRuntimeException
```
    Natural logarithm.
    
    Parameters:
    
    x - The operand.
    
    Returns:
    
    The natural logarithm of x.
    
    Throws:
    
    java.lang.ArithmeticException - If x is less than or equal to zero.
    
    ApfloatRuntimeException
  - log
```
public Apfloat log(Apfloat x,
                   Apfloat b)
            throws java.lang.ArithmeticException,
                   ApfloatRuntimeException
```
    Logarithm in specified base.
    
    Parameters:
    
    x - The operand.
    
    b - The base.
    
    Returns:
    
    The base-b logarithm of x.
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                    ApfloatRuntimeException
```
    Square root.
    
    Parameters:
    
    x - The operand.
    
    Returns:
    
    The square root of x.
    
    Throws:
    
    java.lang.ArithmeticException - If x is negative.
    
    ApfloatRuntimeException
  - tan
```
public Apfloat tan(Apfloat x)
            throws java.lang.ArithmeticException,
                   ApfloatRuntimeException
```
    Tangent.
    
    Parameters:
    
    x - The operand.
    
    Returns:
    
    The tangent of x.
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
    Inverse root.
    
    Parameters:
    
    x - The operand.
    
    n - Which inverse root to take.
    
    Returns:
    
    x^-1/n.
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                    ApfloatRuntimeException
```
    Root.
    
    Parameters:
    
    x - The operand.
    
    n - Which root to take.
    
    Returns:
    
    x^1/n.
    
    Throws:
    
    java.lang.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,
                     java.math.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,
                                java.math.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:
    
    java.lang.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,
                              java.math.RoundingMode roundingMode)
                       throws ApfloatRuntimeException,
                              java.lang.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:
    
    java.lang.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,
                             java.math.RoundingMode roundingMode)
                      throws ApfloatRuntimeException,
                             java.lang.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:
    
    java.lang.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,
                               java.math.RoundingMode roundingMode)
                        throws ApfloatRuntimeException,
                               java.lang.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:
    
    java.lang.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 java.lang.ArithmeticException,
                     ApfloatRuntimeException
```
    Angle of point.
    
    Parameters:
    
    x - The operand.
    
    y - The operand.
    
    Returns:
    
    The angle of the point (y, x).
    
    Throws:
    
    java.lang.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:
    
    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:
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - pi
```
public Apfloat pi()
           throws ApfloatRuntimeException
```
    π.
    
    Overrides:
    
    pi in class FixedPrecisionApcomplexHelper
    
    Returns:
    
    π.
    
    Throws:
    
    ApfloatRuntimeException
  - pi
```
public Apfloat pi(int radix)
           throws java.lang.NumberFormatException,
                  ApfloatRuntimeException
```
    π.
    
    Overrides:
    
    pi in class FixedPrecisionApcomplexHelper
    
    Parameters:
    
    radix - The radix of the result.
    
    Returns:
    
    π.
    
    Throws:
    
    java.lang.NumberFormatException - If the radix is invalid.
    
    ApfloatRuntimeException
  - logRadix
```
public Apfloat logRadix(int radix)
                 throws java.lang.NumberFormatException,
                        ApfloatRuntimeException
```
    Logarithm.
    
    Parameters:
    
    radix - The radix of the result.
    
    Returns:
    
    log(radix).
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                     ApfloatRuntimeException
```
    Gamma function.
    
    Parameters:
    
    x - The operand.
    
    Returns:
    
    Γ(x).
    
    Throws:
    
    java.lang.ArithmeticException - If x is a nonpositive integer.
    
    ApfloatRuntimeException
    
    Since:
    
    1.9.0
  - gamma
```
public Apfloat gamma(Apfloat a,
                     Apfloat x)
              throws java.lang.ArithmeticException,
                     ApfloatRuntimeException
```
    Incomplete gamma function.
    
    Parameters:
    
    a - The first operand.
    
    x - The second operand.
    
    Returns:
    
    Γ(a, x).
    
    Throws:
    
    java.lang.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 java.lang.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:
    
    java.lang.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 java.lang.ArithmeticException,
                        ApfloatRuntimeException
```
    Logarithm of the gamma function.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    logΓ(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is nonpositive.
    
    ApfloatRuntimeException
    
    Since:
    
    1.11.0
  - digamma
```
public Apfloat digamma(Apfloat x)
                throws java.lang.ArithmeticException,
                       ApfloatRuntimeException
```
    Digamma function.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    ψ(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is a nonpositive integer.
    
    ApfloatRuntimeException
    
    Since:
    
    1.11.0
  - polygamma
```
public Apfloat polygamma(long n,
                         Apfloat x)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException
```
    Polygamma function.
    
    Parameters:
    
    n - The order.
    
    x - The argument.
    
    Returns:
    
    ψ⁽ⁿ⁾(x)
    
    Throws:
    
    java.lang.ArithmeticException - If n is negative or x is a nonpositive integer.
    
    ApfloatRuntimeException
    
    Since:
    
    1.13.0
  - beta
```
public Apfloat beta(Apfloat a,
                    Apfloat b)
             throws java.lang.ArithmeticException,
                    ApfloatRuntimeException
```
    Beta function.
    
    Parameters:
    
    a - The first argument.
    
    b - The second argument.
    
    Returns:
    
    B(a, b)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                    ApfloatRuntimeException
```
    Incomplete beta function.
    
    Parameters:
    
    x - The first argument.
    
    a - The second argument.
    
    b - The third argument.
    
    Returns:
    
    B_x(a, b)
    
    Throws:
    
    java.lang.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 java.lang.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:
    
    java.lang.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 java.lang.ArithmeticException,
                          ApfloatRuntimeException
```
    Pochhammer symbol.
    
    Parameters:
    
    x - The first argument.
    
    n - The second argument.
    
    Returns:
    
    (x)_n
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                        ApfloatRuntimeException
```
    Binomial coefficient.
    
    Parameters:
    
    n - The argument.
    
    k - The argument.
    
    Returns:
    
    The binomial coefficient.
    
    Throws:
    
    java.lang.ArithmeticException - If n, k or n - k is a nonpositive integer.
    
    ApfloatRuntimeException
    
    Since:
    
    1.11.0
  - zeta
```
public Apfloat zeta(Apfloat s)
             throws java.lang.ArithmeticException,
                    ApfloatRuntimeException
```
    Riemann zeta function.
    
    Parameters:
    
    s - The argument.
    
    Returns:
    
    ζ(s)
    
    Throws:
    
    java.lang.ArithmeticException - If s is 1.
    
    ApfloatRuntimeException
    
    Since:
    
    1.11.0
  - zeta
```
public Apfloat zeta(Apfloat s,
                    Apfloat a)
             throws java.lang.ArithmeticException,
                    ApfloatRuntimeException
```
    Hurwitz zeta function.
    
    Parameters:
    
    s - The first argument.
    
    a - The second argument.
    
    Returns:
    
    ζ(s, a)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                                 ApfloatRuntimeException
```
    Confluent hypergeometric function ₀F₁.
    
    Parameters:
    
    a - The first argument.
    
    x - The second argument.
    
    Returns:
    
    ₀F₁(; a; x)
    
    Throws:
    
    java.lang.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 java.lang.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:
    
    java.lang.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 java.lang.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:
    
    java.lang.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 java.lang.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:
    
    java.lang.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 java.lang.ArithmeticException,
                          ApfloatRuntimeException
```
    Inverse error function.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    erf⁻¹(x)
    
    Throws:
    
    java.lang.ArithmeticException - If |x| is ≥ 1.
    
    ApfloatRuntimeException
    
    Since:
    
    1.13.0
  - inverseErfc
```
public Apfloat inverseErfc(Apfloat x)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
    Inverse complementary error function.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    erfc⁻¹(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is ≤ 0 or ≥ 2.
    
    ApfloatRuntimeException
    
    Since:
    
    1.13.0
  - 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 java.lang.ArithmeticException,
                            ApfloatRuntimeException
```
    Exponential integral E.
    
    Parameters:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    E_ν(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                             ApfloatRuntimeException
```
    Exponential integral Ei.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    Ei(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is zero.
    
    ApfloatRuntimeException
    
    Since:
    
    1.13.0
  - logIntegral
```
public Apfloat logIntegral(Apfloat x)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
    Logarithmic integral.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    li(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
    Cosine integral.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    Ci(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                            ApfloatRuntimeException
```
    Hyperbolic cosine integral.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    Chi(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                       ApfloatRuntimeException
```
    Bessel function of the first kind.
    
    Parameters:
    
    \u03bd - The order.
    
    x - The argument.
    
    Returns:
    
    J_ν(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                       ApfloatRuntimeException
```
    Modified Bessel function of the first kind.
    
    Parameters:
    
    \u03bd - The order.
    
    x - The argument.
    
    Returns:
    
    I_ν(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                       ApfloatRuntimeException
```
    Bessel function of the second kind.
    
    Parameters:
    
    \u03bd - The order.
    
    x - The argument.
    
    Returns:
    
    Y_ν(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is ≤ 0.
    
    ApfloatRuntimeException
    
    Since:
    
    1.13.0
  - besselK
```
public Apfloat besselK(Apfloat ν,
                       Apfloat x)
                throws java.lang.ArithmeticException,
                       ApfloatRuntimeException
```
    Modified Bessel function of the second kind.
    
    Parameters:
    
    \u03bd - The order.
    
    x - The argument.
    
    Returns:
    
    K_ν(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is ≤ 0.
    
    ApfloatRuntimeException
    
    Since:
    
    1.13.0
  - ellipticK
```
public Apfloat ellipticK(Apfloat x)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException
```
    Complete elliptic integral of the first kind.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    K(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is ≥ 1.
    
    ApfloatRuntimeException
    
    Since:
    
    1.13.0
  - ellipticE
```
public Apfloat ellipticE(Apfloat x)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException
```
    Complete elliptic integral of the second kind.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    E(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is > 1.
    
    ApfloatRuntimeException
    
    Since:
    
    1.13.0
  - hermiteH
```
public Apfloat hermiteH(Apfloat ν,
                        Apfloat x)
                 throws ApfloatRuntimeException
```
    Hermite function.
    
    Parameters:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    H_ν(x)
    
    Throws:
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - laguerreL
```
public Apfloat laguerreL(Apfloat ν,
                         Apfloat x)
                  throws ApfloatRuntimeException
```
    Laguerre function.
    
    Parameters:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    L_ν(x)
    
    Throws:
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - laguerreL
```
public Apfloat laguerreL(Apfloat ν,
                         Apfloat λ,
                         Apfloat x)
                  throws ApfloatRuntimeException
```
    Generalized Laguerre function.
    
    Parameters:
    
    \u03bd - The first argument.
    
    \u03bb - The second argument.
    
    x - The third argument.
    
    Returns:
    
    L_ν^λ(x)
    
    Throws:
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - legendreP
```
public Apfloat legendreP(Apfloat ν,
                         Apfloat x)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException
```
    Legendre function.
    
    Parameters:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    P_ν(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                         ApfloatRuntimeException
```
    Associated Legendre function of the first kind.
    
    Parameters:
    
    \u03bd - The first argument.
    
    \u03bc - The second argument.
    
    x - The third argument.
    
    Returns:
    
    P_ν^μ(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                         ApfloatRuntimeException
```
    Legendre function of the second kind.
    
    Parameters:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    Q_ν(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is ≥ 1 or ≤ -1.
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - legendreQ
```
public Apfloat legendreQ(Apfloat ν,
                         Apfloat μ,
                         Apfloat x)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException
```
    Associated Legendre function of the second kind.
    
    Parameters:
    
    \u03bd - The first argument.
    
    \u03bc - The second argument.
    
    x - The third argument.
    
    Returns:
    
    Q_ν^μ(x)
    
    Throws:
    
    java.lang.ArithmeticException - If x is ≥ 1 or ≤ -1.
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - chebyshevT
```
public Apfloat chebyshevT(Apfloat ν,
                          Apfloat x)
                   throws java.lang.ArithmeticException,
                          ApfloatRuntimeException
```
    Chebyshev function of the first kind.
    
    Parameters:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    T_ν(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                          ApfloatRuntimeException
```
    Chebyshev function of the second kind.
    
    Parameters:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    U_ν(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
    Renormalized Gegenbauer function.
    
    Parameters:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    C_ν⁽⁰⁾(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
    Gegenbauer function.
    
    Parameters:
    
    \u03bd - The first argument.
    
    \u03bb - The second argument.
    
    x - The third argument.
    
    Returns:
    
    C_ν^λ(x)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                       ApfloatRuntimeException
```
    Jacobi function.
    
    Parameters:
    
    \u03bd - The first argument.
    
    a - The second argument.
    
    b - The third argument.
    
    x - The fourth argument.
    
    Returns:
    
    P_ν^(a,b)(x)
    
    Throws:
    
    java.lang.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:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    F_ν(x)
    
    Throws:
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - eulerE
```
public Apfloat eulerE(long n,
                      Apfloat x)
               throws java.lang.IllegalArgumentException,
                      ApfloatRuntimeException
```
    Euler polynomial.
    
    Parameters:
    
    n - The first argument.
    
    x - The second argument.
    
    Returns:
    
    E_n(x)
    
    Throws:
    
    java.lang.IllegalArgumentException - If n < 0.
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - bernoulliB
```
public Apfloat bernoulliB(long n,
                          Apfloat x)
                   throws java.lang.IllegalArgumentException,
                          ApfloatRuntimeException
```
    Bernoulli polynomial.
    
    Parameters:
    
    n - The first argument.
    
    x - The second argument.
    
    Returns:
    
    B_n(x)
    
    Throws:
    
    java.lang.IllegalArgumentException - If n < 0.
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - harmonicNumber
```
public Apfloat harmonicNumber(Apfloat x)
                       throws java.lang.ArithmeticException,
                              ApfloatRuntimeException
```
    Harmonic number.
    
    Parameters:
    
    x - The argument.
    
    Returns:
    
    H_x
    
    Throws:
    
    java.lang.ArithmeticException - If x is a negative integer.
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - harmonicNumber
```
public Apfloat harmonicNumber(Apfloat x,
                              Apfloat r)
                       throws java.lang.ArithmeticException,
                              ApfloatRuntimeException
```
    Generalized harmonic number.
    
    Parameters:
    
    x - The first argument.
    
    r - The second argument.
    
    Returns:
    
    H_x^(r)
    
    Throws:
    
    java.lang.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 java.lang.ArithmeticException,
                       ApfloatRuntimeException
```
    Polylogarithm.
    
    Parameters:
    
    \u03bd - The first argument.
    
    x - The second argument.
    
    Returns:
    
    Li_ν(x)
    
    Throws:
    
    java.lang.ArithmeticException - If ν is ≤ 1 and x is 1 or if x is > 1.
    
    ApfloatRuntimeException
    
    Since:
    
    1.14.0
  - 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 java.lang.NumberFormatException,
                      ApfloatRuntimeException
```
    Return a uniformly distributed random number 0 ≤ x < 1.
    
    Parameters:
    
    radix - The radix of the number.
    
    Returns:
    
    A random number.
    
    Throws:
    
    java.lang.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 java.lang.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:
    
    java.lang.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:
    
    java.lang.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:
    
    java.lang.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
  - setPrecision
```
private Apfloat setPrecision(Apfloat x)
                      throws ApfloatRuntimeException
```
    Throws:
    
    ApfloatRuntimeException
  - setPrecision
```
private Apfloat[] setPrecision(Apfloat[] x)
                        throws ApfloatRuntimeException
```
    Throws:
    
    ApfloatRuntimeException
  - checkSmallLinear
```
private Apfloat checkSmallLinear(Apfloat x)
```

Class FixedPrecisionApfloatHelper

Constructor Summary

Method Summary

Methods inherited from class org.apfloat.FixedPrecisionApcomplexHelper

Methods inherited from class java.lang.Object

Constructor Detail

FixedPrecisionApfloatHelper

Method Detail

valueOf

negate

add

subtract

multiply

divide

pow

pow

abs

acos

acosh

asin

asinh

atan

atanh

cbrt

cos

cosh

exp

log

log

sin

sinh

sqrt

tan

tanh

sinc

agm

inverseRoot

root

scale

mod

ceil

floor

truncate

frac

round

roundToPrecision

roundToInteger

roundToPlaces

roundToMultiple

w

toDegrees

toRadians

atan2

copySign

fmod

modf

factorial

factorial

doubleFactorial

doubleFactorial

pi

pi

logRadix

multiplyAdd

multiplySubtract

product

sum

gamma

gamma

gamma

logGamma

digamma

polygamma

beta

beta

beta

pochhammer

binomial

zeta

zeta