java.lang.Object
- org.apfloat.ApfloatMath

```
public class ApfloatMath
extends java.lang.Object
```
Various mathematical functions for arbitrary precision floating-point numbers.
Due to different types of round-off errors that can occur in the implementation, no guarantees about e.g. monotonicity are given for any of the methods.

Version:

1.14.0

See Also:

ApintMath

Nested Class Summary

Nested Classes
Modifier and Type	Class	Description
`(package private) static class`	`ApfloatMath.ApfloatHolder`	Simple JavaBean to hold one apfloat.
`private static class`	`ApfloatMath.PiCalculator`

Field Summary

Fields
Modifier and Type	Field	Description
`private static java.util.Map<java.lang.Integer,Apfloat>`	`nextGaussian`
`private static java.util.Map<java.lang.Integer,java.lang.Long>`	`nextGaussianPrecision`
`private static java.util.concurrent.ConcurrentMap<java.lang.Integer,java.lang.Object>`	`radixGaussianKeys`
`private static java.util.Map<java.lang.Integer,Apfloat>`	`radixLog`
`private static java.util.concurrent.ConcurrentMap<java.lang.Integer,java.lang.Object>`	`radixLogKeys`
`private static java.util.Map<java.lang.Integer,Apfloat>`	`radixLogPi`
`private static java.util.Map<java.lang.Integer,Apfloat>`	`radixPi`
`private static java.util.Map<java.lang.Integer,ApfloatMath.PiCalculator>`	`radixPiCalculator`
`private static java.util.Map<java.lang.Integer,Apfloat>`	`radixPiInverseRoot`
`private static java.util.concurrent.ConcurrentMap<java.lang.Integer,java.lang.Object>`	`radixPiKeys`
`private static java.util.Map<java.lang.Integer,Apfloat>`	`radixPiP`
`private static java.util.Map<java.lang.Integer,Apfloat>`	`radixPiQ`
`private static java.util.Map<java.lang.Integer,Apfloat>`	`radixPiT`
`private static java.util.Map<java.lang.Integer,java.lang.Long>`	`radixPiTerms`
`private static java.util.Map<java.lang.Integer,Apfloat>`	`SHUTDOWN_MAP`

Constructor Summary

Constructors
Modifier Constructor Description

private ApfloatMath()

Method Summary

All Methods Static Methods Concrete Methods Deprecated Methods
Modifier and Type	Method	Description
`static Apfloat`	`abs(Apfloat x)`	Absolute value.
`static Apfloat`	`acos(Apfloat x)`	Inverse cosine.
`(package private) static Apfloat`	`acos(Apfloat x, long precision)`
`static Apfloat`	`acosh(Apfloat x)`	Inverse hyperbolic cosine.
`static Apfloat`	`agm(Apfloat a, Apfloat b)`	Arithmetic-geometric mean.
`(package private) static Apfloat`	`agm(Apfloat a, Apfloat b, java.util.function.Consumer<Apfloat> consumer)`
`private static Apfloat`	`agmConsume(java.util.function.Consumer<Apfloat> consumer, Apfloat a, Apfloat c2, long workingPrecision)`
`static Apfloat`	`airyAi(Apfloat x)`	Airy function Ai.
`(package private) static Apfloat`	`airyAi(Apfloat x, long precision)`
`static Apfloat`	`airyAiPrime(Apfloat x)`	Derivative of the Airy function Ai.
`(package private) static Apfloat`	`airyAiPrime(Apfloat x, long precision)`
`static Apfloat`	`airyBi(Apfloat x)`	Airy function Bi.
`(package private) static Apfloat`	`airyBi(Apfloat x, long precision)`
`static Apfloat`	`airyBiPrime(Apfloat x)`	Derivative of the Airy function Bi.
`(package private) static Apfloat`	`airyBiPrime(Apfloat x, long precision)`
`static Apfloat`	`asin(Apfloat x)`	Inverse sine.
`static Apfloat`	`asinh(Apfloat x)`	Inverse hyperbolic sine.
`static Apfloat`	`atan(Apfloat x)`	Inverse tangent.
`static Apfloat`	`atan2(Apfloat y, Apfloat x)`	Converts cartesian coordinates to polar coordinates.
`static Apfloat`	`atanh(Apfloat x)`	Inverse hyperbolic tangent.
`static Apfloat`	`bernoulliB(long n, Apfloat x)`	Bernoulli polynomial.
`(package private) static Apfloat`	`bernoulliB(long n, Apfloat x, long precision)`
`static Apfloat`	`besselI(Apfloat ν, Apfloat x)`	Modified Bessel function of the first kind.
`static Apfloat`	`besselJ(Apfloat ν, Apfloat x)`	Bessel function of the first kind.
`static Apfloat`	`besselK(Apfloat ν, Apfloat x)`	Modified Bessel function of the second kind.
`static Apfloat`	`besselY(Apfloat ν, Apfloat x)`	Bessel function of the second kind.
`static Apfloat`	`beta(Apfloat a, Apfloat b)`	Beta function.
`static Apfloat`	`beta(Apfloat x, Apfloat a, Apfloat b)`	Incomplete beta function.
`static Apfloat`	`beta(Apfloat x1, Apfloat x2, Apfloat a, Apfloat b)`	Generalized incomplete beta function.
`static Apfloat`	`binomial(Apfloat n, Apfloat k)`	Binomial coefficient.
`private static Apfloat`	`calculatePi(long precision, int radix)`
`static Apfloat`	`catalan(long precision)`	Calculates Catalan's constant, G.
`static Apfloat`	`catalan(long precision, int radix)`	Calculates Catalan's constant, G.
`static Apfloat`	`cbrt(Apfloat x)`	Cube root.
`static Apint`	`ceil(Apfloat x)`	Ceiling function.
`static Apfloat`	`chebyshevT(Apfloat ν, Apfloat x)`	Chebyshev function of the first kind.
`static Apfloat`	`chebyshevU(Apfloat ν, Apfloat x)`	Chebyshev function of the second kind.
`private static void`	`checkHypergeometric2F1(Apfloat a, Apfloat b, Apfloat x)`
`private static void`	`checkMinusOneNonInteger(Apfloat ν, Apfloat x)`
`(package private) static void`	`cleanUp()`
`static Apint[]`	`continuedFraction(Apfloat x, int n)`	Generates the first `n` terms in the continued fraction representation of `x`.
`static Aprational[]`	`convergents(Apfloat x, int n)`	Generates the first `n` convergents corresponding to the continued fraction of `x`.
`static Apfloat`	`copySign(Apfloat x, Apfloat y)`	Copy sign from one argument to another.
`static Apfloat`	`cos(Apfloat x)`	Cosine.
`static Apfloat`	`cosh(Apfloat x)`	Hyperbolic cosine.
`static Apfloat`	`coshIntegral(Apfloat x)`	Hyperbolic cosine integral.
`static Apfloat`	`cosIntegral(Apfloat x)`	Cosine integral.
`static Apfloat`	`digamma(Apfloat x)`	Digamma function.
`(package private) static Apfloat`	`doubleFactorial(long n, long precision)`
`(package private) static Apfloat`	`doubleFactorial(long n, long precision, int radix)`
`static Apfloat`	`e(long precision)`	Calculates e.
`static Apfloat`	`e(long precision, int radix)`	Calculates e.
`private static Apfloat[]`	`e(long start, long end, long precision, int radix)`
`static Apfloat`	`ellipticE(Apfloat x)`	Complete elliptic integral of the second kind.
`(package private) static Apfloat`	`ellipticE(Apfloat x, long precision)`
`static Apfloat`	`ellipticK(Apfloat x)`	Complete elliptic integral of the first kind.
`(package private) static Apfloat`	`ellipticK(Apfloat x, long precision)`
`static Apfloat`	`erf(Apfloat x)`	Error function.
`static Apfloat`	`erfc(Apfloat x)`	Complementary error function.
`(package private) static Apfloat`	`erfcFixedPrecision(Apfloat x)`
`(package private) static Apfloat`	`erfFixedPrecision(Apfloat x)`
`static Apfloat`	`erfi(Apfloat x)`	Imaginary error function.
`(package private) static Apfloat`	`erfiFixedPrecision(Apfloat x)`
`static Apfloat`	`euler(long precision)`	Calculates γ, the Euler-Mascheroni constant.
`static Apfloat`	`euler(long precision, int radix)`	Calculates γ, the Euler-Mascheroni constant.
`static Apfloat`	`eulerE(long n, Apfloat x)`	Euler polynomial.
`(package private) static Apfloat`	`eulerE(long n, Apfloat x, long precision)`
`(package private) static Apfloat`	`eulerSmall(long precision, int radix)`
`static Apfloat`	`exp(Apfloat x)`	Exponent function.
`static Apfloat`	`expIntegralE(Apfloat ν, Apfloat x)`	Exponential integral E.
`static Apfloat`	`expIntegralEi(Apfloat x)`	Exponential integral Ei.
`(package private) static Apfloat`	`factorial(long n, long precision)`
`(package private) static Apfloat`	`factorial(long n, long precision, int radix)`
`static Apfloat`	`fibonacci(Apfloat ν, Apfloat x)`	Fibonacci function.
`static Apint`	`floor(Apfloat x)`	Floor function.
`static Apfloat`	`fmod(Apfloat x, Apfloat y)`	Returns x modulo y.
`static Apfloat`	`frac(Apfloat x)`	Extracts fractional part.
`static Apfloat`	`fresnelC(Apfloat x)`	Fresnel integral C.
`static Apfloat`	`fresnelS(Apfloat x)`	Fresnel integral S.
`static Apfloat`	`gamma(Apfloat x)`	Gamma function.
`static Apfloat`	`gamma(Apfloat a, Apfloat x)`	Incomplete gamma function.
`static Apfloat`	`gamma(Apfloat a, Apfloat x0, Apfloat x1)`	Generalized incomplete gamma function.
`static Apfloat`	`gegenbauerC(Apfloat ν, Apfloat x)`	Renormalized Gegenbauer function.
`static Apfloat`	`gegenbauerC(Apfloat ν, Apfloat λ, Apfloat x)`	Gegenbauer function.
`private static java.lang.Object`	`getRadixKey(java.util.Map<java.lang.Integer,java.lang.Object> radixKeys, int radix)`
`static Apfloat`	`glaisher(long precision)`	Calculates the Glaisher‐Kinkelin constant, A.
`static Apfloat`	`glaisher(long precision, int radix)`	Calculates the Glaisher‐Kinkelin constant, A.
`(package private) static Apfloat`	`halfPi(int radix, long precision)`
`static Apfloat`	`harmonicNumber(Apfloat x)`	Harmonic number.
`static Apfloat`	`harmonicNumber(Apfloat x, Apfloat r)`	Generalized harmonic number.
`static Apfloat`	`hermiteH(Apfloat ν, Apfloat x)`	Hermite function.
`static Apfloat`	`hypergeometric0F1(Apfloat a, Apfloat x)`	Confluent hypergeometric function ₀F₁.
`static Apfloat`	`hypergeometric0F1Regularized(Apfloat a, Apfloat x)`	Regularized confluent hypergeometric function ₀F̃₁.
`static Apfloat`	`hypergeometric1F1(Apfloat a, Apfloat b, Apfloat x)`	Kummer confluent hypergeometric function ₁F₁.
`static Apfloat`	`hypergeometric1F1Regularized(Apfloat a, Apfloat b, Apfloat x)`	Regularized Kummer confluent hypergeometric function ₁F̃₁.
`static Apfloat`	`hypergeometric2F1(Apfloat a, Apfloat b, Apfloat c, Apfloat x)`	Hypergeometric function ₂F₁.
`static Apfloat`	`hypergeometric2F1Regularized(Apfloat a, Apfloat b, Apfloat c, Apfloat x)`	Regularized hypergeometric function ₂F̃₁.
`static Apfloat`	`hypergeometricU(Apfloat a, Apfloat b, Apfloat x)`	Tricomi's confluent hypergeometric function U.
`static Apfloat`	`inverseErf(Apfloat x)`	Inverse error function.
`static Apfloat`	`inverseErfc(Apfloat x)`	Inverse complementary error function.
`private static long`	`inverseFactorial(long precision, int radix)`
`static Apfloat`	`inverseRoot(Apfloat x, long n)`	Inverse positive integer root.
`static Apfloat`	`inverseRoot(Apfloat x, long n, long targetPrecision)`	Inverse positive integer root.
`static Apfloat`	`inverseRoot(Apfloat x, long n, long targetPrecision, Apfloat initialGuess)`	Inverse positive integer root.
`static Apfloat`	`inverseRoot(Apfloat x, long n, long targetPrecision, Apfloat initialGuess, long initialPrecision)`	Inverse positive integer root.
`private static boolean`	`isEven(Apfloat x)`
`static Apfloat`	`jacobiP(Apfloat ν, Apfloat a, Apfloat b, Apfloat x)`	Jacobi function.
`static Apfloat`	`khinchin(long precision)`	Calculates Khinchin's constant, K.Uses the default radix.
`static Apfloat`	`khinchin(long precision, int radix)`	Calculates Khinchin's constant, K.
`static Apfloat`	`laguerreL(Apfloat ν, Apfloat x)`	Laguerre function.
`static Apfloat`	`laguerreL(Apfloat ν, Apfloat λ, Apfloat x)`	Generalized Laguerre function.
`private static Apfloat`	`lastIterationExtendPrecision(int iterations, int precisingIteration, Apfloat x)`
`static Apfloat`	`legendreP(Apfloat ν, Apfloat x)`	Legendre function.
`static Apfloat`	`legendreP(Apfloat ν, Apfloat μ, Apfloat x)`	Associated Legendre function of the first kind.
`static Apfloat`	`legendreQ(Apfloat ν, Apfloat x)`	Legendre function of the second kind.
`static Apfloat`	`legendreQ(Apfloat ν, Apfloat μ, Apfloat x)`	Associated Legendre function of the second kind.
`static Apfloat`	`log(Apfloat x)`	Natural logarithm.
`private static Apfloat`	`log(Apfloat x, boolean multiplyByPi)`
`static Apfloat`	`log(Apfloat x, Apfloat b)`	Logarithm in arbitrary base.
`static Apfloat`	`logGamma(Apfloat x)`	Logarithm of the gamma function.
`static Apfloat`	`logIntegral(Apfloat x)`	Logarithmic integral.
`static Apfloat`	`logisticSigmoid(Apfloat x)`	Logistic sigmoid.
`static Apfloat`	`logRadix(long precision, int radix)`	Gets or calculates logarithm of a radix to required precision.
`private static Apfloat`	`logRadix(long precision, int radix, boolean multiplyByPi)`
`static Apfloat`	`max(Apfloat x, Apfloat y)`	Returns the greater of the two values.
`static Apfloat`	`min(Apfloat x, Apfloat y)`	Returns the smaller of the two values.
`static Apfloat[]`	`modf(Apfloat x)`	Split to integer and fractional parts.
`static Apfloat`	`multiplyAdd(Apfloat a, Apfloat b, Apfloat c, Apfloat d)`	Fused multiply-add.
`private static Apfloat`	`multiplyAddOrSubtract(Apfloat a, Apfloat b, Apfloat c, Apfloat d, boolean subtract)`
`static Apfloat`	`multiplySubtract(Apfloat a, Apfloat b, Apfloat c, Apfloat d)`	Fused multiply-subtract.
`static Apfloat`	`negate(Apfloat x)`	Deprecated. Use `Apfloat.negate()`.
`static Apfloat`	`nextAfter(Apfloat start, Apfloat direction)`	Returns the number adjacent to the first argument in the direction of the second argument, considering the scale and precision of the first argument.
`static Apfloat`	`nextDown(Apfloat x)`	Returns the number adjacent to the argument in the direction of negative infinity, considering the scale and precision of the argument.
`private static Apfloat`	`nextInDirection(Apfloat x, int direction)`
`static Apfloat`	`nextUp(Apfloat x)`	Returns the number adjacent to the argument in the direction of positive infinity, considering the scale and precision of the argument.
`private static Apfloat`	`oddProduct(long n, long m, long precision, int radix)`
`static Apfloat`	`pi(long precision)`	Calculates π.
`static Apfloat`	`pi(long precision, int radix)`	Calculates π.
`static Apfloat`	`pochhammer(Apfloat x, Apfloat n)`	Pochhammer symbol.
`static Apfloat`	`polygamma(long n, Apfloat x)`	Polygamma function.
`static Apfloat`	`polylog(Apfloat ν, Apfloat x)`	Polylogarithm.
`static Apfloat`	`pow(Apfloat x, long n)`	Integer power.
`static Apfloat`	`pow(Apfloat x, Apfloat y)`	Arbitrary power.
`static Apfloat`	`product(Apfloat... x)`	Product of numbers.
`static Apfloat`	`random(long digits)`	Generates a random number.
`static Apfloat`	`random(long digits, int radix)`	Generates a random number.
`static Apfloat`	`randomGaussian(long digits)`	Generates a random, Gaussian ("normally") distributed number value with mean 0 and standard deviation 1.
`static Apfloat`	`randomGaussian(long digits, int radix)`	Generates a random, Gaussian ("normally") distributed number value with mean 0 and standard deviation 1.
`private static Apfloat`	`rawLog(Apfloat x, boolean multiplyByPi)`
`static Apfloat`	`root(Apfloat x, long n)`	Positive integer root.
`static Apfloat`	`round(Apfloat x, long precision, java.math.RoundingMode roundingMode)`	Deprecated. Use `roundToPrecision(Apfloat,long,RoundingMode)`.
`static Apint`	`roundToInteger(Apfloat x, java.math.RoundingMode roundingMode)`	Rounds `x` to integer using the specified rounding mode.
`static Apfloat`	`roundToMultiple(Apfloat x, Apfloat y, java.math.RoundingMode roundingMode)`	Rounds `x` to the nearest multiple of `y` using the specified rounding mode.
`static Apfloat`	`roundToPlaces(Apfloat x, long places, java.math.RoundingMode roundingMode)`	Rounds `x` to the specified number of places using the specified rounding mode.
`static Apfloat`	`roundToPrecision(Apfloat x, long precision, java.math.RoundingMode roundingMode)`	Rounds the given number to the specified precision with the specified rounding mode.
`static Apfloat`	`scale(Apfloat x, long scale)`	Multiply by a power of the radix.
`static Apfloat`	`sin(Apfloat x)`	Sine.
`static Apfloat`	`sinc(Apfloat x)`	Sinc.
`static Apfloat`	`sinh(Apfloat x)`	Hyperbolic sine.
`static Apfloat`	`sinhIntegral(Apfloat x)`	Hyperbolic sine integral.
`static Apfloat`	`sinIntegral(Apfloat x)`	Sine integral.
`static Apfloat`	`sqrt(Apfloat x)`	Square root.
`static Apfloat`	`sum(Apfloat... x)`	Sum of numbers.
`static Apfloat`	`tan(Apfloat x)`	Tangent.
`static Apfloat`	`tanh(Apfloat x)`	Hyperbolic tangent.
`private static Apfloat`	`tanh(Apfloat x, boolean negate)`
`(package private) static Apfloat`	`tanhFixedPrecision(Apfloat x)`
`static Apfloat`	`toDegrees(Apfloat x)`	Converts an angle measured in radians to degrees.
`static Apfloat`	`toRadians(Apfloat x)`	Converts an angle measured in degrees to radians.
`static Apint`	`truncate(Apfloat x)`	Truncates fractional part.
`static Apfloat`	`ulp(Apfloat x)`	Returns the unit in the last place of the argument, considering the scale and precision.
`private static Apfloat`	`ulp(Apfloat x, int direction)`
`static Apfloat`	`w(Apfloat x)`	Lambert W function.
`static Apfloat`	`zeta(Apfloat s)`	Riemann zeta function.
`static Apfloat`	`zeta(Apfloat s, Apfloat a)`	Hurwitz zeta function.

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

Field Detail

SHUTDOWN_MAP

private static final java.util.Map<java.lang.Integer,Apfloat> SHUTDOWN_MAP

radixPiKeys

private static java.util.concurrent.ConcurrentMap<java.lang.Integer,java.lang.Object> radixPiKeys

radixPi

private static java.util.Map<java.lang.Integer,Apfloat> radixPi

radixPiCalculator

private static java.util.Map<java.lang.Integer,ApfloatMath.PiCalculator> radixPiCalculator

radixPiT

private static java.util.Map<java.lang.Integer,Apfloat> radixPiT

radixPiQ

private static java.util.Map<java.lang.Integer,Apfloat> radixPiQ

radixPiP

private static java.util.Map<java.lang.Integer,Apfloat> radixPiP

radixPiInverseRoot

private static java.util.Map<java.lang.Integer,Apfloat> radixPiInverseRoot

radixPiTerms

private static java.util.Map<java.lang.Integer,java.lang.Long> radixPiTerms

radixLogKeys

private static java.util.concurrent.ConcurrentMap<java.lang.Integer,java.lang.Object> radixLogKeys

radixLog

private static java.util.Map<java.lang.Integer,Apfloat> radixLog

radixLogPi

private static java.util.Map<java.lang.Integer,Apfloat> radixLogPi

radixGaussianKeys

private static java.util.concurrent.ConcurrentMap<java.lang.Integer,java.lang.Object> radixGaussianKeys

nextGaussian

private static java.util.Map<java.lang.Integer,Apfloat> nextGaussian

nextGaussianPrecision

private static java.util.Map<java.lang.Integer,java.lang.Long> nextGaussianPrecision

Constructor Detail
- ApfloatMath
```
private ApfloatMath()
```

Method Detail
- pow
```
public static Apfloat pow(Apfloat x,
                          long n)
                   throws java.lang.ArithmeticException,
                          ApfloatRuntimeException
```
  Integer power.
  
  Parameters:
  
  x - Base of the power operator.
  
  n - Exponent of the power operator.
  
  Returns:
  
  x to the n:th power, that is xⁿ.
  
  Throws:
  
  java.lang.ArithmeticException - If both x and n are zero.
  
  ApfloatRuntimeException
- sqrt
```
public static Apfloat sqrt(Apfloat x)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
  Square root.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Square root of x.
  
  Throws:
  
  java.lang.ArithmeticException - If x is negative.
  
  ApfloatRuntimeException
- cbrt
```
public static Apfloat cbrt(Apfloat x)
                    throws ApfloatRuntimeException
```
  Cube root.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Cube root of x.
  
  Throws:
  
  ApfloatRuntimeException
- root
```
public static Apfloat root(Apfloat x,
                           long n)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
  Positive integer root.
  
  Parameters:
  
  x - The argument.
  
  n - Which root to take.
  
  Returns:
  
  n:th root of x, that is x^1/n.
  
  Throws:
  
  java.lang.ArithmeticException - If n is zero, or x is negative and n is even.
  
  ApfloatRuntimeException
- inverseRoot
```
public static Apfloat inverseRoot(Apfloat x,
                                  long n)
                           throws java.lang.ArithmeticException,
                                  ApfloatRuntimeException
```
  Inverse positive integer root.
  
  Parameters:
  
  x - The argument.
  
  n - Which inverse root to take.
  
  Returns:
  
  Inverse n:th root of x, that is x^-1/n.
  
  Throws:
  
  java.lang.ArithmeticException - If x or n is zero, or x is negative and n is even.
  
  ApfloatRuntimeException
- inverseRoot
```
public static Apfloat inverseRoot(Apfloat x,
                                  long n,
                                  long targetPrecision)
                           throws java.lang.IllegalArgumentException,
                                  java.lang.ArithmeticException,
                                  ApfloatRuntimeException
```
  Inverse positive integer root.
  
  Parameters:
  
  x - The argument.
  
  n - Which inverse root to take.
  
  targetPrecision - Precision of the desired result.
  
  Returns:
  
  Inverse n:th root of x, that is x^-1/n.
  
  Throws:
  
  java.lang.IllegalArgumentException - If targetPrecision <= 0.
  
  java.lang.ArithmeticException - If x or n is zero, or x is negative and n is even.
  
  ApfloatRuntimeException
- inverseRoot
```
public static Apfloat inverseRoot(Apfloat x,
                                  long n,
                                  long targetPrecision,
                                  Apfloat initialGuess)
                           throws java.lang.IllegalArgumentException,
                                  java.lang.ArithmeticException,
                                  ApfloatRuntimeException
```
  Inverse positive integer root.
  
  Parameters:
  
  x - The argument.
  
  n - Which inverse root to take.
  
  targetPrecision - Precision of the desired result.
  
  initialGuess - Initial guess for the result value, or null if none is available.
  
  Returns:
  
  Inverse n:th root of x, that is x^-1/n.
  
  Throws:
  
  java.lang.IllegalArgumentException - If targetPrecision <= 0.
  
  java.lang.ArithmeticException - If x or n is zero, or x is negative and n is even.
  
  ApfloatRuntimeException
- inverseRoot
```
public static Apfloat inverseRoot(Apfloat x,
                                  long n,
                                  long targetPrecision,
                                  Apfloat initialGuess,
                                  long initialPrecision)
                           throws java.lang.IllegalArgumentException,
                                  java.lang.ArithmeticException,
                                  ApfloatRuntimeException
```
  Inverse positive integer root.
  This method is the basis for most of apfloat's non-elementary operations. It is used e.g. in Apfloat.divide(Apfloat), sqrt(Apfloat) and root(Apfloat,long).
  
  Parameters:
  
  x - The argument.
  
  n - Which inverse root to take.
  
  targetPrecision - Precision of the desired result.
  
  initialGuess - Initial guess for the result value, or null if none is available.
  
  initialPrecision - Precision of the initial guess, if available.
  
  Returns:
  
  Inverse n:th root of x, that is x^-1/n.
  
  Throws:
  
  java.lang.IllegalArgumentException - If targetPrecision <= 0 or initialPrecision <= 0.
  
  java.lang.ArithmeticException - If x or n is zero, or x is negative and n is even.
  
  ApfloatRuntimeException
- floor
```
public static Apint floor(Apfloat x)
                   throws ApfloatRuntimeException
```
  Floor function. Returns the largest (closest to positive infinity) value that is not greater than the argument and is equal to a mathematical integer.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  x rounded towards negative infinity.
  
  Throws:
  
  ApfloatRuntimeException
- ceil
```
public static Apint ceil(Apfloat x)
                  throws ApfloatRuntimeException
```
  Ceiling function. Returns the smallest (closest to negative infinity) value that is not less than the argument and is equal to a mathematical integer.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  x rounded towards positive infinity.
  
  Throws:
  
  ApfloatRuntimeException
- truncate
```
public static Apint truncate(Apfloat x)
                      throws ApfloatRuntimeException
```
  Truncates fractional part.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  x rounded towards zero.
  
  Throws:
  
  ApfloatRuntimeException
- frac
```
public static Apfloat frac(Apfloat x)
                    throws ApfloatRuntimeException
```
  Extracts fractional part.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  The fractional part of x.
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.7.0
- round
```
@Deprecated
public static Apfloat round(Apfloat x,
                            long precision,
                            java.math.RoundingMode roundingMode)
                     throws java.lang.IllegalArgumentException,
                            java.lang.ArithmeticException,
                            ApfloatRuntimeException
```
  Deprecated.
  Use roundToPrecision(Apfloat,long,RoundingMode).
  
  Rounds the given number to the specified precision with the specified rounding mode.
  
  Parameters:
  
  x - The number to round.
  
  precision - The precision to round to.
  
  roundingMode - The rounding mode to use.
  
  Returns:
  
  The rounded number.
  
  Throws:
  
  java.lang.IllegalArgumentException - If precision is less than zero or zero.
  
  java.lang.ArithmeticException - If rounding is necessary (result is not exact) and rounding mode is RoundingMode.UNNECESSARY.
  
  ApfloatRuntimeException
  
  Since:
  
  1.7.0
- roundToPrecision
```
public static Apfloat roundToPrecision(Apfloat x,
                                       long precision,
                                       java.math.RoundingMode roundingMode)
                                throws java.lang.IllegalArgumentException,
                                       java.lang.ArithmeticException,
                                       ApfloatRuntimeException
```
  Rounds the given number to the specified precision with the specified rounding mode.
  
  Parameters:
  
  x - The number to round.
  
  precision - The precision to round to.
  
  roundingMode - The rounding mode to use.
  
  Returns:
  
  The rounded number.
  
  Throws:
  
  java.lang.IllegalArgumentException - If precision is less than zero or zero.
  
  java.lang.ArithmeticException - If rounding is necessary (result is not exact) and rounding mode is RoundingMode.UNNECESSARY.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- roundToInteger
```
public static Apint roundToInteger(Apfloat x,
                                   java.math.RoundingMode roundingMode)
                            throws java.lang.IllegalArgumentException,
                                   java.lang.ArithmeticException,
                                   ApfloatRuntimeException
```
  Rounds x to integer using the specified rounding mode.
  
  Parameters:
  
  x - The number to round.
  
  roundingMode - The rounding mode to use.
  
  Returns:
  
  The rounded number.
  
  Throws:
  
  java.lang.ArithmeticException - If rounding is necessary (result is not exact) and rounding mode is RoundingMode.UNNECESSARY.
  
  java.lang.IllegalArgumentException
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- roundToPlaces
```
public static Apfloat roundToPlaces(Apfloat x,
                                    long places,
                                    java.math.RoundingMode roundingMode)
                             throws java.lang.IllegalArgumentException,
                                    java.lang.ArithmeticException,
                                    ApfloatRuntimeException
```
  Rounds x to the specified number of places using the specified rounding mode.
  
  Parameters:
  
  x - The number to round.
  
  places - The number of places to round to (in base 10, the number of decimal places).
  
  roundingMode - The rounding mode to use.
  
  Returns:
  
  The rounded number.
  
  Throws:
  
  java.lang.ArithmeticException - If rounding is necessary (result is not exact) and rounding mode is RoundingMode.UNNECESSARY.
  
  java.lang.IllegalArgumentException
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- roundToMultiple
```
public static Apfloat roundToMultiple(Apfloat x,
                                      Apfloat y,
                                      java.math.RoundingMode roundingMode)
                               throws java.lang.IllegalArgumentException,
                                      java.lang.ArithmeticException,
                                      ApfloatRuntimeException
```
  Rounds x to the nearest multiple of y using the specified rounding mode.
  
  Parameters:
  
  x - The number to round.
  
  y - The integer multiple to round to.
  
  roundingMode - The rounding mode to use.
  
  Returns:
  
  The rounded number.
  
  Throws:
  
  java.lang.ArithmeticException - If rounding is necessary (result is not exact) and rounding mode is RoundingMode.UNNECESSARY.
  
  java.lang.IllegalArgumentException
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- negate
```
@Deprecated
public static Apfloat negate(Apfloat x)
                      throws ApfloatRuntimeException
```
  Deprecated.
  Use Apfloat.negate().
  
  Returns an apfloat whose value is -x.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  -x.
  
  Throws:
  
  ApfloatRuntimeException
- abs
```
public static Apfloat abs(Apfloat x)
                   throws ApfloatRuntimeException
```
  Absolute value.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Absolute value of x.
  
  Throws:
  
  ApfloatRuntimeException
- copySign
```
public static Apfloat copySign(Apfloat x,
                               Apfloat y)
                        throws ApfloatRuntimeException
```
  Copy sign from one argument to another.
  
  Parameters:
  
  x - The value whose sign is to be adjusted.
  
  y - The value whose sign is to be used.
  
  Returns:
  
  x with its sign changed to match the sign of y.
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.1
- scale
```
public static Apfloat scale(Apfloat x,
                            long scale)
                     throws ApfloatRuntimeException
```
  Multiply by a power of the radix.
  
  Parameters:
  
  x - The argument.
  
  scale - The scaling factor.
  
  Returns:
  
  x * x.radix()^scale.
  
  Throws:
  
  ApfloatRuntimeException
- modf
```
public static Apfloat[] modf(Apfloat x)
                      throws ApfloatRuntimeException
```
  Split to integer and fractional parts. The integer part is simply i = floor(x). For the fractional part f the following is always true:
  0 <= f < 1
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  An array of two apfloats, [i, f], the first being the integer part and the last being the fractional part.
  
  Throws:
  
  ApfloatRuntimeException
- fmod
```
public static Apfloat fmod(Apfloat x,
                           Apfloat y)
                    throws ApfloatRuntimeException
```
  Returns x modulo y.
  This function calculates the remainder f of x / y such that x = i * y + f, where i is an integer, f has the same sign as x, and the absolute value of f is less than the absolute value of y.
  If y is zero, then zero is returned.
  
  Parameters:
  
  x - The dividend.
  
  y - The divisor.
  
  Returns:
  
  The remainder when x is divided by y.
  
  Throws:
  
  ApfloatRuntimeException
- multiplyAdd
```
public static Apfloat multiplyAdd(Apfloat a,
                                  Apfloat b,
                                  Apfloat c,
                                  Apfloat d)
                           throws ApfloatRuntimeException
```
  Fused multiply-add. Calculates a * b + c * d so that the precision used in the multiplications is only what is needed for the end result. Performance can this way be better than by calculating a.multiply(b).add(c.multiply(d)).
  
  Parameters:
  
  a - First argument.
  
  b - Second argument.
  
  c - Third argument.
  
  d - Fourth argument.
  
  Returns:
  
  a * b + c * d.
  
  Throws:
  
  ApfloatRuntimeException
- multiplySubtract
```
public static Apfloat multiplySubtract(Apfloat a,
                                       Apfloat b,
                                       Apfloat c,
                                       Apfloat d)
                                throws ApfloatRuntimeException
```
  Fused multiply-subtract. Calculates a * b - c * d so that the precision used in the multiplications is only what is needed for the end result. Performance can this way be better than by calculating a.multiply(b).subtract(c.multiply(d)).
  
  Parameters:
  
  a - First argument.
  
  b - Second argument.
  
  c - Third argument.
  
  d - Fourth argument.
  
  Returns:
  
  a * b - c * d.
  
  Throws:
  
  ApfloatRuntimeException
- multiplyAddOrSubtract
```
private static Apfloat multiplyAddOrSubtract(Apfloat a,
                                             Apfloat b,
                                             Apfloat c,
                                             Apfloat d,
                                             boolean subtract)
                                      throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- agm
```
public static Apfloat agm(Apfloat a,
                          Apfloat b)
                   throws ApfloatRuntimeException
```
  Arithmetic-geometric mean.
  
  Parameters:
  
  a - First argument.
  
  b - Second argument.
  
  Returns:
  
  Arithmetic-geometric mean of a and b.
  
  Throws:
  
  ApfloatRuntimeException
- agm
```
static Apfloat agm(Apfloat a,
                   Apfloat b,
                   java.util.function.Consumer<Apfloat> consumer)
            throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- agmConsume
```
private static Apfloat agmConsume(java.util.function.Consumer<Apfloat> consumer,
                                  Apfloat a,
                                  Apfloat c2,
                                  long workingPrecision)
```
- pi
```
public static Apfloat pi(long precision)
                  throws java.lang.IllegalArgumentException,
                         java.lang.NumberFormatException,
                         ApfloatRuntimeException
```
  Calculates π. Uses default radix.
  
  Parameters:
  
  precision - Number of digits of π to calculate.
  
  Returns:
  
  π accurate to precision digits, in the default radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the default radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
- pi
```
public static Apfloat pi(long precision,
                         int radix)
                  throws java.lang.IllegalArgumentException,
                         java.lang.NumberFormatException,
                         ApfloatRuntimeException
```
  Calculates π.
  
  Parameters:
  
  precision - Number of digits of π to calculate.
  
  radix - The radix in which the number should be presented.
  
  Returns:
  
  π accurate to precision digits, in base radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
- calculatePi
```
private static Apfloat calculatePi(long precision,
                                   int radix)
                            throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- log
```
public static Apfloat log(Apfloat x)
                   throws java.lang.ArithmeticException,
                          ApfloatRuntimeException
```
  Natural logarithm.
  The logarithm is calculated using the arithmetic-geometric mean. See the Borweins' book for the formula.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Natural logarithm of x.
  
  Throws:
  
  java.lang.ArithmeticException - If x <= 0.
  
  ApfloatRuntimeException
- log
```
public static Apfloat log(Apfloat x,
                          Apfloat b)
                   throws java.lang.ArithmeticException,
                          ApfloatRuntimeException
```
  Logarithm in arbitrary base.
  The logarithm is calculated using the arithmetic-geometric mean. See the Borweins' book for the formula.
  
  Parameters:
  
  x - The argument.
  
  b - The base.
  
  Returns:
  
  Base-b logarithm of x.
  
  Throws:
  
  java.lang.ArithmeticException - If x <= 0 or b <= 0.
  
  ApfloatRuntimeException
  
  Since:
  
  1.6
- log
```
private static Apfloat log(Apfloat x,
                           boolean multiplyByPi)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
  Throws:
  
  java.lang.ArithmeticException
  
  ApfloatRuntimeException
- rawLog
```
private static Apfloat rawLog(Apfloat x,
                              boolean multiplyByPi)
                       throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- logRadix
```
public static Apfloat logRadix(long precision,
                               int radix)
                        throws ApfloatRuntimeException
```
  Gets or calculates logarithm of a radix to required precision. The calculated value is stored in a cache for later usage.
  
  Parameters:
  
  precision - The needed precision.
  
  radix - The radix.
  
  Returns:
  
  Natural logarithm of radix to the specified precision.
  
  Throws:
  
  java.lang.NumberFormatException - If the radix is invalid.
  
  ApfloatRuntimeException
- logRadix
```
private static Apfloat logRadix(long precision,
                                int radix,
                                boolean multiplyByPi)
                         throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- exp
```
public static Apfloat exp(Apfloat x)
                   throws ApfloatRuntimeException
```
  Exponent function. Calculated using Newton's iteration for the inverse of logarithm.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  e^x.
  
  Throws:
  
  ApfloatRuntimeException
- pow
```
public static Apfloat pow(Apfloat x,
                          Apfloat y)
                   throws java.lang.ArithmeticException,
                          ApfloatRuntimeException
```
  Arbitrary power. Calculated using log() and exp().
  
  Parameters:
  
  x - The base.
  
  y - The exponent.
  
  Returns:
  
  x^y.
  
  Throws:
  
  java.lang.ArithmeticException - If both x and y are zero, or x is negative and y is not an integer.
  
  ApfloatRuntimeException
- acosh
```
public static Apfloat acosh(Apfloat x)
                     throws java.lang.ArithmeticException,
                            ApfloatRuntimeException
```
  Inverse hyperbolic cosine. Calculated using log().
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Inverse hyperbolic cosine of x.
  
  Throws:
  
  java.lang.ArithmeticException - If x < 1.
  
  ApfloatRuntimeException
- asinh
```
public static Apfloat asinh(Apfloat x)
                     throws ApfloatRuntimeException
```
  Inverse hyperbolic sine. Calculated using log().
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Inverse hyperbolic sine of x.
  
  Throws:
  
  ApfloatRuntimeException
- atanh
```
public static Apfloat atanh(Apfloat x)
                     throws java.lang.ArithmeticException,
                            ApfloatRuntimeException
```
  Inverse hyperbolic tangent. Calculated using log().
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Inverse hyperbolic tangent of x.
  
  Throws:
  
  java.lang.ArithmeticException - If abs(x) >= 1.
  
  ApfloatRuntimeException
- cosh
```
public static Apfloat cosh(Apfloat x)
                    throws ApfloatRuntimeException
```
  Hyperbolic cosine. Calculated using exp().
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Hyperbolic cosine of x.
  
  Throws:
  
  ApfloatRuntimeException
- sinh
```
public static Apfloat sinh(Apfloat x)
                    throws ApfloatRuntimeException
```
  Hyperbolic sine. Calculated using exp().
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Hyperbolic sine of x.
  
  Throws:
  
  ApfloatRuntimeException
- tanh
```
public static Apfloat tanh(Apfloat x)
                    throws ApfloatRuntimeException
```
  Hyperbolic tangent. Calculated using exp().
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Hyperbolic tangent of x.
  
  Throws:
  
  ApfloatRuntimeException
- tanhFixedPrecision
```
static Apfloat tanhFixedPrecision(Apfloat x)
                           throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- tanh
```
private static Apfloat tanh(Apfloat x,
                            boolean negate)
                     throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- acos
```
public static Apfloat acos(Apfloat x)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
  Inverse cosine. Calculated using complex functions.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Inverse cosine of x.
  
  Throws:
  
  java.lang.ArithmeticException - If abs(x) > 1.
  
  ApfloatRuntimeException
- acos
```
static Apfloat acos(Apfloat x,
                    long precision)
```
- halfPi
```
static Apfloat halfPi(int radix,
                      long precision)
```
- asin
```
public static Apfloat asin(Apfloat x)
                    throws java.lang.ArithmeticException,
                           ApfloatRuntimeException
```
  Inverse sine. Calculated using complex functions.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Inverse sine of x.
  
  Throws:
  
  java.lang.ArithmeticException - If abs(x) > 1.
  
  ApfloatRuntimeException
- atan
```
public static Apfloat atan(Apfloat x)
                    throws ApfloatRuntimeException
```
  Inverse tangent. Calculated using complex functions.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Inverse tangent of x.
  
  Throws:
  
  ApfloatRuntimeException
- atan2
```
public static Apfloat atan2(Apfloat y,
                            Apfloat x)
                     throws java.lang.ArithmeticException,
                            ApfloatRuntimeException
```
  Converts cartesian coordinates to polar coordinates. Calculated using complex functions.
  Computes the phase angle by computing an arc tangent of y/x in the range of -π < angle <= π.
  
  Parameters:
  
  y - The argument.
  
  x - The argument.
  
  Returns:
  
  The angle of the point (x, y) in the plane.
  
  Throws:
  
  java.lang.ArithmeticException - If y and x are both zero.
  
  ApfloatRuntimeException
- cos
```
public static Apfloat cos(Apfloat x)
                   throws ApfloatRuntimeException
```
  Cosine. Calculated using complex functions.
  
  Parameters:
  
  x - The argument (in radians).
  
  Returns:
  
  Cosine of x.
  
  Throws:
  
  ApfloatRuntimeException
- sin
```
public static Apfloat sin(Apfloat x)
                   throws ApfloatRuntimeException
```
  Sine. Calculated using complex functions.
  
  Parameters:
  
  x - The argument (in radians).
  
  Returns:
  
  Sine of x.
  
  Throws:
  
  ApfloatRuntimeException
- tan
```
public static Apfloat tan(Apfloat x)
                   throws java.lang.ArithmeticException,
                          ApfloatRuntimeException
```
  Tangent. Calculated using complex functions.
  
  Parameters:
  
  x - The argument (in radians).
  
  Returns:
  
  Tangent of x.
  
  Throws:
  
  java.lang.ArithmeticException - If x is π/2 + n π where n is an integer.
  
  ApfloatRuntimeException
- sinc
```
public static Apfloat sinc(Apfloat x)
                    throws ApfloatRuntimeException
```
  Sinc.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  sinc(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.14.0
- w
```
public static Apfloat w(Apfloat x)
                 throws java.lang.ArithmeticException,
                        ApfloatRuntimeException
```
  Lambert W function. The W function gives the solution to the equation W e^W = x. Also known as the product logarithm.
  This function only gives the solution to the principal branch, W₀. For the real-valued W_-1 branch, use ApcomplexMath.w(Apcomplex,long).
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  W₀(x).
  
  Throws:
  
  java.lang.ArithmeticException - If x is less than -1/e.
  
  ApfloatRuntimeException
  
  Since:
  
  1.8.0
- toDegrees
```
public static Apfloat toDegrees(Apfloat x)
                         throws ApfloatRuntimeException
```
  Converts an angle measured in radians to degrees.
  
  Parameters:
  
  x - The angle, in radians.
  
  Returns:
  
  The angle in degrees.
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.8.0
- toRadians
```
public static Apfloat toRadians(Apfloat x)
                         throws ApfloatRuntimeException
```
  Converts an angle measured in degrees to radians.
  
  Parameters:
  
  x - The angle, in degrees.
  
  Returns:
  
  The angle in radians.
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.8.0
- product
```
public static Apfloat product(Apfloat... x)
                       throws ApfloatRuntimeException
```
  Product of numbers. The precision used in the multiplications is only what is needed for the end result. This method may perform significantly better than simply multiplying the numbers sequentially.
  If there are no arguments, the return value is 1.
  
  Parameters:
  
  x - The argument(s).
  
  Returns:
  
  The product of the given numbers.
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.3
- sum
```
public static Apfloat sum(Apfloat... x)
                   throws ApfloatRuntimeException
```
  Sum of numbers. The precision used in the additions is only what is needed for the end result. This method may perform significantly better than simply adding the numbers sequentially.
  If there are no arguments, the return value is 0.
  
  Parameters:
  
  x - The argument(s).
  
  Returns:
  
  The sum of the given numbers.
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.3
- e
```
public static Apfloat e(long precision)
                 throws java.lang.IllegalArgumentException,
                        java.lang.NumberFormatException,
                        ApfloatRuntimeException
```
  Calculates e. Uses default radix.
  
  Parameters:
  
  precision - Number of digits of e to calculate.
  
  Returns:
  
  e accurate to precision digits, in the default radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the default radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- e
```
public static Apfloat e(long precision,
                        int radix)
                 throws java.lang.IllegalArgumentException,
                        java.lang.NumberFormatException,
                        ApfloatRuntimeException
```
  Calculates e.
  
  Parameters:
  
  precision - Number of digits of e to calculate.
  
  radix - The radix in which the number should be presented.
  
  Returns:
  
  e accurate to precision digits, in base radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- inverseFactorial
```
private static long inverseFactorial(long precision,
                                     int radix)
```
- e
```
private static Apfloat[] e(long start,
                           long end,
                           long precision,
                           int radix)
```
- euler
```
public static Apfloat euler(long precision)
                     throws java.lang.IllegalArgumentException,
                            java.lang.NumberFormatException,
                            ApfloatRuntimeException
```
  Calculates γ, the Euler-Mascheroni constant. Uses default radix.
  
  Parameters:
  
  precision - Number of digits of γ to calculate.
  
  Returns:
  
  γ accurate to precision digits, in the default radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the default radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.10.0
- euler
```
public static Apfloat euler(long precision,
                            int radix)
                     throws java.lang.IllegalArgumentException,
                            java.lang.NumberFormatException,
                            ApfloatRuntimeException
```
  Calculates γ, the Euler-Mascheroni constant.
  
  Parameters:
  
  precision - Number of digits of γ to calculate.
  
  radix - The radix in which the number should be presented.
  
  Returns:
  
  γ accurate to precision digits, in base radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.10.0
- eulerSmall
```
static Apfloat eulerSmall(long precision,
                          int radix)
                   throws java.lang.IllegalArgumentException,
                          java.lang.NumberFormatException,
                          ApfloatRuntimeException
```
  Throws:
  
  java.lang.IllegalArgumentException
  
  java.lang.NumberFormatException
  
  ApfloatRuntimeException
- catalan
```
public static Apfloat catalan(long precision)
                       throws java.lang.IllegalArgumentException,
                              java.lang.NumberFormatException,
                              ApfloatRuntimeException
```
  Calculates Catalan's constant, G. Uses the default radix.
  
  Parameters:
  
  precision - Number of digits of G to calculate.
  
  Returns:
  
  G accurate to precision digits, in the default radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the default radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- catalan
```
public static Apfloat catalan(long precision,
                              int radix)
                       throws java.lang.IllegalArgumentException,
                              java.lang.NumberFormatException,
                              ApfloatRuntimeException
```
  Calculates Catalan's constant, G. Uses the specified radix.
  
  Parameters:
  
  precision - Number of digits of G to calculate.
  
  radix - The radix in which the number should be presented.
  
  Returns:
  
  G accurate to precision digits, in base radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- glaisher
```
public static Apfloat glaisher(long precision)
                        throws java.lang.IllegalArgumentException,
                               java.lang.NumberFormatException,
                               ApfloatRuntimeException
```
  Calculates the Glaisher‐Kinkelin constant, A. Uses the default radix.
  
  Parameters:
  
  precision - Number of digits of A to calculate.
  
  Returns:
  
  A accurate to precision digits, in the default radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the default radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- glaisher
```
public static Apfloat glaisher(long precision,
                               int radix)
                        throws java.lang.IllegalArgumentException,
                               java.lang.NumberFormatException,
                               ApfloatRuntimeException
```
  Calculates the Glaisher‐Kinkelin constant, A. Uses the specified radix.
  
  Parameters:
  
  precision - Number of digits of A to calculate.
  
  radix - The radix in which the number should be presented.
  
  Returns:
  
  A accurate to precision digits, in base radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- khinchin
```
public static Apfloat khinchin(long precision)
                        throws java.lang.IllegalArgumentException,
                               java.lang.NumberFormatException,
                               ApfloatRuntimeException
```
  Calculates Khinchin's constant, K.Uses the default radix.
  
  Parameters:
  
  precision - Number of digits of K to calculate.
  
  Returns:
  
  K accurate to precision digits, in the default radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the default radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- khinchin
```
public static Apfloat khinchin(long precision,
                               int radix)
                        throws java.lang.IllegalArgumentException,
                               java.lang.NumberFormatException,
                               ApfloatRuntimeException
```
  Calculates Khinchin's constant, K. Uses the specified radix.
  
  Parameters:
  
  precision - Number of digits of K to calculate.
  
  radix - The radix in which the number should be presented.
  
  Returns:
  
  K accurate to precision digits, in base radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the radix is not valid.
  
  java.lang.IllegalArgumentException - In case the precision is invalid.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- gamma
```
public static Apfloat gamma(Apfloat x)
                     throws java.lang.ArithmeticException,
                            ApfloatRuntimeException
```
  Gamma function.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Γ(x)
  
  Throws:
  
  java.lang.ArithmeticException - If x is a nonpositive integer.
  
  ApfloatRuntimeException
  
  Since:
  
  1.9.0
- gamma
```
public static Apfloat gamma(Apfloat a,
                            Apfloat x)
                     throws java.lang.ArithmeticException,
                            ApfloatRuntimeException
```
  Incomplete gamma function.
  
  Parameters:
  
  a - The first argument.
  
  x - The second argument.
  
  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 static Apfloat gamma(Apfloat a,
                            Apfloat x0,
                            Apfloat x1)
                     throws java.lang.ArithmeticException,
                            ApfloatRuntimeException
```
  Generalized incomplete gamma function.
  This function is defined as: Γ(a, x0, x1) = Γ(a, x0) - Γ(a, x1)
  The lower gamma function can be calculated with: γ(a, x) = Γ(a, 0, x)
  
  Parameters:
  
  a - The first argument.
  
  x0 - The second argument.
  
  x1 - The third argument.
  
  Returns:
  
  Γ(a, x0, 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 static 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 static 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 static 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 static 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 static 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 static 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 static 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 static Apfloat binomial(Apfloat n,
                               Apfloat k)
                        throws java.lang.ArithmeticException,
                               ApfloatRuntimeException
```
  Binomial coefficient. Calculated using the gamma(Apfloat) function.
  
  Parameters:
  
  n - The first argument.
  
  k - The second argument.
  
  Returns:
  
  $(\binom{n}{k})$
  
  Throws:
  
  java.lang.ArithmeticException - If n is a negative integer and k is noninteger.
  
  ApfloatRuntimeException
  
  Since:
  
  1.11.0
- zeta
```
public static 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 static 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 static 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 static 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 static Apfloat hypergeometric1F1(Apfloat a,
                                        Apfloat b,
                                        Apfloat x)
                                 throws java.lang.ArithmeticException,
                                        ApfloatRuntimeException
```
  Kummer confluent hypergeometric function ₁F₁. Also known as the confluent hypergeometric function of the first kind.
  
  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 static Apfloat hypergeometric1F1Regularized(Apfloat a,
                                                   Apfloat b,
                                                   Apfloat x)
                                            throws ApfloatRuntimeException
```
  Regularized Kummer confluent hypergeometric function ₁F̃₁. Also known as the regularized confluent hypergeometric function of the first kind.
  
  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 static Apfloat hypergeometric2F1(Apfloat a,
                                        Apfloat b,
                                        Apfloat c,
                                        Apfloat x)
                                 throws java.lang.ArithmeticException,
                                        ApfloatRuntimeException
```
  Hypergeometric function ₂F₁. Also known as the Gaussian or ordinary hypergeometric function.
  
  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
- checkHypergeometric2F1
```
private static void checkHypergeometric2F1(Apfloat a,
                                           Apfloat b,
                                           Apfloat x)
                                    throws java.lang.ArithmeticException,
                                           ApfloatRuntimeException
```
  Throws:
  
  java.lang.ArithmeticException
  
  ApfloatRuntimeException
- hypergeometric2F1Regularized
```
public static Apfloat hypergeometric2F1Regularized(Apfloat a,
                                                   Apfloat b,
                                                   Apfloat c,
                                                   Apfloat x)
                                            throws ApfloatRuntimeException
```
  Regularized hypergeometric function ₂F̃₁. Also known as the regularized Gaussian or ordinary hypergeometric function.
  
  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 static Apfloat hypergeometricU(Apfloat a,
                                      Apfloat b,
                                      Apfloat x)
                               throws java.lang.ArithmeticException,
                                      ApfloatRuntimeException
```
  Tricomi's confluent hypergeometric function U. Also known as the confluent hypergeometric function of the second kind.
  
  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 static Apfloat erf(Apfloat x)
                   throws ApfloatRuntimeException
```
  Error function.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  erf(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- erfFixedPrecision
```
static Apfloat erfFixedPrecision(Apfloat x)
                          throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- erfc
```
public static Apfloat erfc(Apfloat x)
                    throws ApfloatRuntimeException
```
  Complementary error function.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  erfc(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- erfcFixedPrecision
```
static Apfloat erfcFixedPrecision(Apfloat x)
                           throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- erfi
```
public static Apfloat erfi(Apfloat x)
                    throws ApfloatRuntimeException
```
  Imaginary error function.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  erfi(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- erfiFixedPrecision
```
static Apfloat erfiFixedPrecision(Apfloat x)
                           throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- inverseErf
```
public static 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 static 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 static Apfloat fresnelS(Apfloat x)
                        throws ApfloatRuntimeException
```
  Fresnel integral S.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  S(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- fresnelC
```
public static Apfloat fresnelC(Apfloat x)
                        throws ApfloatRuntimeException
```
  Fresnel integral C.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  C(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- expIntegralE
```
public static 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 static 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 static 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 static Apfloat sinIntegral(Apfloat x)
                           throws ApfloatRuntimeException
```
  Sine integral.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Si(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- cosIntegral
```
public static 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 static Apfloat sinhIntegral(Apfloat x)
                            throws ApfloatRuntimeException
```
  Hyperbolic sine integral.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Shi(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- coshIntegral
```
public static 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 static Apfloat airyAi(Apfloat x)
                      throws ApfloatRuntimeException
```
  Airy function Ai.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Ai(x)
  
  Throws:
  
  InfiniteExpansionException - If x is zero.
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- airyAi
```
static Apfloat airyAi(Apfloat x,
                      long precision)
               throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- airyAiPrime
```
public static Apfloat airyAiPrime(Apfloat x)
                           throws ApfloatRuntimeException
```
  Derivative of the Airy function Ai.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Ai′(x)
  
  Throws:
  
  InfiniteExpansionException - If x is zero.
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- airyAiPrime
```
static Apfloat airyAiPrime(Apfloat x,
                           long precision)
                    throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- airyBi
```
public static Apfloat airyBi(Apfloat x)
                      throws ApfloatRuntimeException
```
  Airy function Bi.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Bi(x)
  
  Throws:
  
  InfiniteExpansionException - If x is zero.
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- airyBi
```
static Apfloat airyBi(Apfloat x,
                      long precision)
               throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- airyBiPrime
```
public static Apfloat airyBiPrime(Apfloat x)
                           throws ApfloatRuntimeException
```
  Derivative of the Airy function Bi.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  Bi′(x)
  
  Throws:
  
  InfiniteExpansionException - If x is zero.
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- airyBiPrime
```
static Apfloat airyBiPrime(Apfloat x,
                           long precision)
                    throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- besselJ
```
public static 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 static 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 static 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 static 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 static Apfloat ellipticK(Apfloat x)
                         throws java.lang.ArithmeticException,
                                ApfloatRuntimeException
```
  Complete elliptic integral of the first kind.
  Note that this function uses the definition: $K (x) ⩵ \int_{0}^{\frac{π}{2}} \frac{1}{\sqrt{1 - x \sin^{2} (t)}} ⅆ t$
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  K(x)
  
  Throws:
  
  InfiniteExpansionException - If x is zero.
  
  java.lang.ArithmeticException - If x is ≥ 1.
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- ellipticK
```
static Apfloat ellipticK(Apfloat x,
                         long precision)
                  throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- ellipticE
```
public static Apfloat ellipticE(Apfloat x)
                         throws java.lang.ArithmeticException,
                                ApfloatRuntimeException
```
  Complete elliptic integral of the second kind.
  Note that this function uses the definition: $E (x) ⩵ \int_{0}^{\frac{π}{2}} \sqrt{1 - x \sin^{2} (t)} ⅆ t$
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  E(x)
  
  Throws:
  
  InfiniteExpansionException - If x is zero.
  
  java.lang.ArithmeticException - If x is > 1.
  
  ApfloatRuntimeException
  
  Since:
  
  1.13.0
- ellipticE
```
static Apfloat ellipticE(Apfloat x,
                         long precision)
                  throws java.lang.ArithmeticException,
                         ApfloatRuntimeException
```
  Throws:
  
  java.lang.ArithmeticException
  
  ApfloatRuntimeException
- hermiteH
```
public static Apfloat hermiteH(Apfloat ν,
                               Apfloat x)
                        throws ApfloatRuntimeException
```
  Hermite function. For integer values of ν gives the Hermite polynomial.
  
  Parameters:
  
  \u03bd - The first argument.
  
  x - The second argument.
  
  Returns:
  
  H_ν(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.14.0
- laguerreL
```
public static Apfloat laguerreL(Apfloat ν,
                                Apfloat x)
                         throws ApfloatRuntimeException
```
  Laguerre function. For integer values of ν gives the Laguerre polynomial.
  
  Parameters:
  
  \u03bd - The first argument.
  
  x - The second argument.
  
  Returns:
  
  L_ν(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.14.0
- laguerreL
```
public static Apfloat laguerreL(Apfloat ν,
                                Apfloat λ,
                                Apfloat x)
                         throws ApfloatRuntimeException
```
  Generalized Laguerre function. For integer values of ν gives the generalized Laguerre polynomial.
  
  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 static Apfloat legendreP(Apfloat ν,
                                Apfloat x)
                         throws java.lang.ArithmeticException,
                                ApfloatRuntimeException
```
  Legendre function. For integer values of ν gives the Legendre polynomial.
  
  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 static Apfloat legendreP(Apfloat ν,
                                Apfloat μ,
                                Apfloat x)
                         throws java.lang.ArithmeticException,
                                ApfloatRuntimeException
```
  Associated Legendre function of the first kind. Gives Legendre functions of type 2.
  
  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
- isEven
```
private static boolean isEven(Apfloat x)
```
- legendreQ
```
public static 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 static Apfloat legendreQ(Apfloat ν,
                                Apfloat μ,
                                Apfloat x)
                         throws java.lang.ArithmeticException,
                                ApfloatRuntimeException
```
  Associated Legendre function of the second kind. Gives Legendre functions of type 2.
  
  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 static Apfloat chebyshevT(Apfloat ν,
                                 Apfloat x)
                          throws java.lang.ArithmeticException,
                                 ApfloatRuntimeException
```
  Chebyshev function of the first kind. For integer values of ν gives the Chebyshev polynomial 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
- checkMinusOneNonInteger
```
private static void checkMinusOneNonInteger(Apfloat ν,
                                            Apfloat x)
```
- chebyshevU
```
public static Apfloat chebyshevU(Apfloat ν,
                                 Apfloat x)
                          throws java.lang.ArithmeticException,
                                 ApfloatRuntimeException
```
  Chebyshev function of the second kind. For integer values of ν gives the Chebyshev polynomial 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 static 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 static Apfloat gegenbauerC(Apfloat ν,
                                  Apfloat λ,
                                  Apfloat x)
                           throws java.lang.ArithmeticException,
                                  ApfloatRuntimeException
```
  Gegenbauer function. For nonnegative integer values of ν gives the Gegenbauer polynomial.
  
  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 static Apfloat jacobiP(Apfloat ν,
                              Apfloat a,
                              Apfloat b,
                              Apfloat x)
                       throws java.lang.ArithmeticException,
                              ApfloatRuntimeException
```
  Jacobi function. For nonnegative integer values of ν gives the Jacobi polynomial.
  
  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 static Apfloat fibonacci(Apfloat ν,
                                Apfloat x)
                         throws ApfloatRuntimeException
```
  Fibonacci function. For nonnegative integer values of ν gives the Fibonacci polynomial.
  
  Parameters:
  
  \u03bd - The first argument.
  
  x - The second argument.
  
  Returns:
  
  F_ν(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.14.0
- eulerE
```
public static 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
- eulerE
```
static Apfloat eulerE(long n,
                      Apfloat x,
                      long precision)
               throws java.lang.IllegalArgumentException,
                      ApfloatRuntimeException
```
  Throws:
  
  java.lang.IllegalArgumentException
  
  ApfloatRuntimeException
- bernoulliB
```
public static 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
- bernoulliB
```
static Apfloat bernoulliB(long n,
                          Apfloat x,
                          long precision)
                   throws java.lang.IllegalArgumentException,
                          ApfloatRuntimeException
```
  Throws:
  
  java.lang.IllegalArgumentException
  
  ApfloatRuntimeException
- harmonicNumber
```
public static 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 static 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 static 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 static Apfloat logisticSigmoid(Apfloat x)
                               throws ApfloatRuntimeException
```
  Logistic sigmoid.
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  σ(x)
  
  Throws:
  
  ApfloatRuntimeException
  
  Since:
  
  1.14.0
- random
```
public static Apfloat random(long digits)
```
  Generates a random number. Uses the default radix. Returned values are chosen pseudorandomly with (approximately) uniform distribution from the range 0 ≤ x < 1. The generated random numbers may have leading zeros and may thus not always have exactly the requested number of significant digits. The precision of the numbers is the requested number of digits minus the number of leading zeros. Trailing zeros do not affect the precision.
  
  Parameters:
  
  digits - Maximum number of digits in the number.
  
  Returns:
  
  A random number, uniformly distributed between 0 ≤ x < 1.
  
  Throws:
  
  java.lang.NumberFormatException - If the default radix is not valid.
  
  java.lang.IllegalArgumentException - In case the number of specified digits is invalid.
  
  Since:
  
  1.9.0
- random
```
public static Apfloat random(long digits,
                             int radix)
```
  Generates a random number. Returned values are chosen pseudorandomly with (approximately) uniform distribution from the range 0 ≤ x < 1. The generated random numbers may have leading zeros and may thus not always have exactly the requested number of significant digits. The precision of the numbers is the requested number of digits minus the number of leading zeros. Trailing zeros do not affect the precision.
  
  Parameters:
  
  digits - Maximum number of digits in the number.
  
  radix - The radix in which the number should be generated.
  
  Returns:
  
  A random number, uniformly distributed between 0 ≤ x < 1, in base radix.
  
  Throws:
  
  java.lang.NumberFormatException - If the radix is not valid.
  
  java.lang.IllegalArgumentException - In case the number of specified digits is invalid.
  
  Since:
  
  1.9.0
- randomGaussian
```
public static Apfloat randomGaussian(long digits)
```
  Generates a random, Gaussian ("normally") distributed number value with mean 0 and standard deviation 1. Uses the default radix.
  
  Parameters:
  
  digits - Maximum number of digits in the number.
  
  Returns:
  
  A random number, Gaussian ("normally") distributed with mean 0 and standard deviation 1.
  
  Throws:
  
  java.lang.NumberFormatException - If the default radix is not valid.
  
  java.lang.IllegalArgumentException - In case the number of specified digits is invalid.
  
  Since:
  
  1.9.0
- randomGaussian
```
public static Apfloat randomGaussian(long digits,
                                     int radix)
```
  Generates a random, Gaussian ("normally") distributed number value with mean 0 and standard deviation 1. Uses the default radix.
  
  Parameters:
  
  digits - Maximum number of digits in the number.
  
  radix - The radix in which the number should be generated.
  
  Returns:
  
  A random number, Gaussian ("normally") distributed with mean 0 and standard deviation 1.
  
  Throws:
  
  java.lang.NumberFormatException - If the radix is not valid.
  
  java.lang.IllegalArgumentException - In case the number of specified digits is invalid.
  
  Since:
  
  1.9.0
- continuedFraction
```
public static Apint[] continuedFraction(Apfloat x,
                                        int n)
```
  Generates the first n terms in the continued fraction representation of x.
  Note that the result length might be less than n, depending on the input value and precision. The last terms could be incorrect due to accumulating round-off errors.
  
  Parameters:
  
  x - The number whose continued fraction terms should be generated.
  
  n - The maximum number of terms to generate.
  
  Returns:
  
  The continued fraction.
  
  Throws:
  
  java.lang.IllegalArgumentException - If n is less than one.
  
  Since:
  
  1.12.0
- convergents
```
public static Aprational[] convergents(Apfloat x,
                                       int n)
```
  Generates the first n convergents corresponding to the continued fraction of x.
  Note that the result length might be less than n, depending on the input value and precision. The last convergents could be incorrect due to accumulating round-off errors.
  
  Parameters:
  
  x - The number whose continued fraction convergents should be generated.
  
  n - The maximum number of convergents to generate.
  
  Returns:
  
  The convergents.
  
  Throws:
  
  java.lang.IllegalArgumentException - If n is less than one.
  
  Since:
  
  1.12.0
- max
```
public static Apfloat max(Apfloat x,
                          Apfloat y)
```
  Returns the greater of the two values.
  
  Parameters:
  
  x - An argument.
  
  y - Another argument.
  
  Returns:
  
  The greater of the two values.
  
  Since:
  
  1.9.0
- min
```
public static Apfloat min(Apfloat x,
                          Apfloat y)
```
  Returns the smaller of the two values.
  
  Parameters:
  
  x - An argument.
  
  y - Another argument.
  
  Returns:
  
  The smaller of the two values.
  
  Since:
  
  1.9.0
- nextAfter
```
public static Apfloat nextAfter(Apfloat start,
                                Apfloat direction)
```
  Returns the number adjacent to the first argument in the direction of the second argument, considering the scale and precision of the first argument. If the precision of the first argument is infinite, the first argument is returned. If both arguments compare as equal then the first argument is returned.
  
  Parameters:
  
  start - The starting value.
  
  direction - Value indicating which of start's neighbors or start should be returned.
  
  Returns:
  
  The number adjacent to start in the direction of direction.
  
  Since:
  
  1.10.0
- nextUp
```
public static Apfloat nextUp(Apfloat x)
```
  Returns the number adjacent to the argument in the direction of positive infinity, considering the scale and precision of the argument. If the precision of the argument is infinite, the argument is returned.
  
  Parameters:
  
  x - The starting value.
  
  Returns:
  
  The adjacent value closer to positive infinity.
  
  Since:
  
  1.10.0
- nextDown
```
public static Apfloat nextDown(Apfloat x)
```
  Returns the number adjacent to the argument in the direction of negative infinity, considering the scale and precision of the argument. If the precision of the argument is infinite, the argument is returned.
  
  Parameters:
  
  x - The starting value.
  
  Returns:
  
  The adjacent value closer to negative infinity.
  
  Since:
  
  1.10.0
- ulp
```
public static Apfloat ulp(Apfloat x)
```
  Returns the unit in the last place of the argument, considering the scale and precision. This is same as the difference between the argument and the value returned from nextUp(Apfloat). If the precision of the argument is infinite, zero is returned.
  For example, ulp of 1. is 1, ulp of 1.1 is 0.1 and ulp of 1.001 is 0.001 (considering significant digits only).
  
  Parameters:
  
  x - The argument.
  
  Returns:
  
  The ulp of the argument.
  
  Since:
  
  1.10.0
- nextInDirection
```
private static Apfloat nextInDirection(Apfloat x,
                                       int direction)
```
- ulp
```
private static Apfloat ulp(Apfloat x,
                           int direction)
```
- lastIterationExtendPrecision
```
private static Apfloat lastIterationExtendPrecision(int iterations,
                                                    int precisingIteration,
                                                    Apfloat x)
                                             throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- getRadixKey
```
private static java.lang.Object getRadixKey(java.util.Map<java.lang.Integer,java.lang.Object> radixKeys,
                                            int radix)
```
- factorial
```
static Apfloat factorial(long n,
                         long precision)
                  throws java.lang.ArithmeticException,
                         java.lang.NumberFormatException,
                         ApfloatRuntimeException
```
  Throws:
  
  java.lang.ArithmeticException
  
  java.lang.NumberFormatException
  
  ApfloatRuntimeException
- factorial
```
static Apfloat factorial(long n,
                         long precision,
                         int radix)
                  throws java.lang.ArithmeticException,
                         java.lang.NumberFormatException,
                         ApfloatRuntimeException
```
  Throws:
  
  java.lang.ArithmeticException
  
  java.lang.NumberFormatException
  
  ApfloatRuntimeException
- oddProduct
```
private static Apfloat oddProduct(long n,
                                  long m,
                                  long precision,
                                  int radix)
                           throws ApfloatRuntimeException
```
  Throws:
  
  ApfloatRuntimeException
- doubleFactorial
```
static Apfloat doubleFactorial(long n,
                               long precision)
                        throws java.lang.ArithmeticException,
                               java.lang.NumberFormatException,
                               ApfloatRuntimeException
```
  Throws:
  
  java.lang.ArithmeticException
  
  java.lang.NumberFormatException
  
  ApfloatRuntimeException
- doubleFactorial
```
static Apfloat doubleFactorial(long n,
                               long precision,
                               int radix)
                        throws java.lang.ArithmeticException,
                               java.lang.NumberFormatException,
                               ApfloatRuntimeException
```
  Throws:
  
  java.lang.ArithmeticException
  
  java.lang.NumberFormatException
  
  ApfloatRuntimeException
- cleanUp
```
static void cleanUp()
```

Class ApfloatMath

Nested Class Summary

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

SHUTDOWN_MAP

radixPiKeys

radixPi

radixPiCalculator

radixPiT

radixPiQ

radixPiP

radixPiInverseRoot

radixPiTerms

radixLogKeys

radixLog

radixLogPi

radixGaussianKeys

nextGaussian

nextGaussianPrecision

Constructor Detail

ApfloatMath

Method Detail

pow

sqrt

cbrt

root

inverseRoot

inverseRoot

inverseRoot

inverseRoot

floor

ceil

truncate

frac

round

roundToPrecision

roundToInteger

roundToPlaces

roundToMultiple

negate

abs

copySign

scale

modf

fmod

multiplyAdd

multiplySubtract

multiplyAddOrSubtract

agm

agm

agmConsume

pi

pi

calculatePi

log

log

log

rawLog

logRadix

logRadix

exp

pow

acosh

asinh

atanh

cosh

sinh

tanh

tanhFixedPrecision

tanh

acos

acos

halfPi

asin

atan

atan2

cos