Package org.apfloat

Class FixedPrecisionApfloatHelper

java.lang.Object

org.apfloat.FixedPrecisionApcomplexHelper

org.apfloat.FixedPrecisionApfloatHelper

public class FixedPrecisionApfloatHelper
extends FixedPrecisionApcomplexHelper

Fixed-precision mathematical functions for floating-point numbers.

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

Since:

1.5

Version:

1.14.0

Author:

Mikko Tommila

Constructor Summary

Constructors

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

Method Summary

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

Methods inherited from class org.apfloat.FixedPrecisionApcomplexHelper

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

Methods inherited from class java.lang.Object

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

Constructor Details

FixedPrecisionApfloatHelper

public FixedPrecisionApfloatHelper(long precision)
                            throws IllegalArgumentException

Constructs an apfloat fixed-precison helper with the specified precision. The results of all mathematical operations are set to the specified precision.

Parameters:

precision - The precision of the results.

Throws:

IllegalArgumentException - In case the precision is invalid.

Method Details

valueOf

public Apfloat valueOf(Apfloat x)

Returns the value with the specified precision.

Parameters:

x - The value.

Returns:

The value with to the specified precision.

negate

public Apfloat negate(Apfloat x)
               throws ApfloatRuntimeException

Negation.

Parameters:

x - The value to negate.

Returns:

-x.

Throws:

ApfloatRuntimeException

add

public Apfloat add(Apfloat x,
 Apfloat y)
            throws ApfloatRuntimeException

Addition.

Parameters:

x - The first operand.

y - The second operand.

Returns:

x + y.

Throws:

ApfloatRuntimeException

subtract

public Apfloat subtract(Apfloat x,
 Apfloat y)
                 throws ApfloatRuntimeException

Subtraction.

Parameters:

x - The first operand.

y - The second operand.

Returns:

x - y.

Throws:

ApfloatRuntimeException

multiply

public Apfloat multiply(Apfloat x,
 Apfloat y)
                 throws ApfloatRuntimeException

Multiplication.

Parameters:

x - The first operand.

y - The second operand.

Returns:

x * y.

Throws:

ApfloatRuntimeException

divide

public Apfloat divide(Apfloat x,
 Apfloat y)
               throws ArithmeticException,
ApfloatRuntimeException

Division.

Parameters:

x - The first operand.

y - The second operand.

Returns:

x / y.

Throws:

ArithmeticException - If y is zero.

ApfloatRuntimeException

pow

public Apfloat pow(Apfloat x,
 Apfloat y)
            throws ArithmeticException,
ApfloatRuntimeException

Power.

Parameters:

x - The first operand.

y - The second operand.

Returns:

xy.

Throws:

ArithmeticException - If x and y are zero, or x is negative and y is not an integer.

ApfloatRuntimeException

pow

public Apfloat pow(Apfloat x,
 long n)
            throws ArithmeticException,
ApfloatRuntimeException

Integer power.

Parameters:

x - The first operand.

n - The second operand.

Returns:

xn.

Throws:

ArithmeticException - If x and n are zero, or x is zero and n is negative.

ApfloatRuntimeException

abs

public Apfloat abs(Apfloat x)
            throws ApfloatRuntimeException

Absolute value.

Parameters:

x - The operand.

Returns:

The absolute value of x.

Throws:

ApfloatRuntimeException

acos

public Apfloat acos(Apfloat x)
             throws ArithmeticException,
ApfloatRuntimeException

Arc cosine.

Parameters:

x - The operand.

Returns:

The arc cosine of x.

Throws:

ArithmeticException - If the absolute value of x is more than one.

ApfloatRuntimeException

acosh

public Apfloat acosh(Apfloat x)
              throws ArithmeticException,
ApfloatRuntimeException

Hyperbolic arc cosine.

Parameters:

x - The operand.

Returns:

The hyperbolic arc cosine of x.

Throws:

ArithmeticException - If the x is less than one.

ApfloatRuntimeException

asin

public Apfloat asin(Apfloat x)
             throws ArithmeticException,
ApfloatRuntimeException

Arc sine.

Parameters:

x - The operand.

Returns:

The arc sine of x.

Throws:

ArithmeticException - If the absolute value of x is more than one.

ApfloatRuntimeException

asinh

public Apfloat asinh(Apfloat x)
              throws ApfloatRuntimeException

Hyperbolic arc sine.

Parameters:

x - The operand.

Returns:

The hyperbolic arc sine of x.

Throws:

ApfloatRuntimeException

atan

public Apfloat atan(Apfloat x)
             throws ApfloatRuntimeException

Arc tangent.

Parameters:

x - The operand.

Returns:

The arc tangent of x.

Throws:

ApfloatRuntimeException

atanh

public Apfloat atanh(Apfloat x)
              throws ArithmeticException,
ApfloatRuntimeException

Hyperbolic arc tangent.

Parameters:

x - The operand.

Returns:

The hyperbolic arc tangent of x.

Throws:

ArithmeticException - If the absolute value of x is equal to or more than one.

ApfloatRuntimeException

cbrt

public Apfloat cbrt(Apfloat x)
             throws ApfloatRuntimeException

Cube root.

Parameters:

x - The operand.

Returns:

The cube root of x.

Throws:

ApfloatRuntimeException

cos

public Apfloat cos(Apfloat x)
            throws ApfloatRuntimeException

Cosine.

Parameters:

x - The operand.

Returns:

The cosine of x.

Throws:

ApfloatRuntimeException

cosh

public Apfloat cosh(Apfloat x)
             throws ApfloatRuntimeException

Hyperbolic cosine.

Parameters:

x - The operand.

Returns:

The hyperbolic cosine of x.

Throws:

ApfloatRuntimeException

exp

public Apfloat exp(Apfloat x)
            throws ApfloatRuntimeException

Exponential function.

Parameters:

x - The operand.

Returns:

ex.

Throws:

ApfloatRuntimeException

log

public Apfloat log(Apfloat x)
            throws ArithmeticException,
ApfloatRuntimeException

Natural logarithm.

Parameters:

x - The operand.

Returns:

The natural logarithm of x.

Throws:

ArithmeticException - If x is less than or equal to zero.

ApfloatRuntimeException

log

public Apfloat log(Apfloat x,
 Apfloat b)
            throws ArithmeticException,
ApfloatRuntimeException

Logarithm in specified base.

Parameters:

x - The operand.

b - The base.

Returns:

The base-b logarithm of x.

Throws:

ArithmeticException - If x or b is less than or equal to zero.

ApfloatRuntimeException

Since:

1.6

sin

public Apfloat sin(Apfloat x)
            throws ApfloatRuntimeException

Sine.

Parameters:

x - The operand.

Returns:

The sine of x.

Throws:

ApfloatRuntimeException

sinh

public Apfloat sinh(Apfloat x)
             throws ApfloatRuntimeException

Hyperbolic sine.

Parameters:

x - The operand.

Returns:

The hyperbolic sine of x.

Throws:

ApfloatRuntimeException

sqrt

public Apfloat sqrt(Apfloat x)
             throws ArithmeticException,
ApfloatRuntimeException

Square root.

Parameters:

x - The operand.

Returns:

The square root of x.

Throws:

ArithmeticException - If x is negative.

ApfloatRuntimeException

tan

public Apfloat tan(Apfloat x)
            throws ArithmeticException,
ApfloatRuntimeException

Tangent.

Parameters:

x - The operand.

Returns:

The tangent of x.

Throws:

ArithmeticException - If x is π/2 + n π where n is an integer.

ApfloatRuntimeException

tanh

public Apfloat tanh(Apfloat x)
             throws ApfloatRuntimeException

Hyperbolic tangent.

Parameters:

x - The operand.

Returns:

The hyperbolic tangent of x.

Throws:

ApfloatRuntimeException

sinc

public Apfloat sinc(Apfloat x)
             throws ApfloatRuntimeException

Sinc.

Parameters:

x - The argument.

Returns:

sinc(x)

Throws:

ApfloatRuntimeException

Since:

1.14.0

agm

public Apfloat agm(Apfloat a,
 Apfloat b)
            throws ApfloatRuntimeException

Arithmetic-geometric mean.

Parameters:

a - The first operand.

b - The first operand.

Returns:

The arithmetic-geometric mean of a and b.

Throws:

ApfloatRuntimeException

inverseRoot

public Apfloat inverseRoot(Apfloat x,
 long n)
                    throws ArithmeticException,
ApfloatRuntimeException

Inverse root.

Parameters:

x - The operand.

n - Which inverse root to take.

Returns:

x-1/n.

Throws:

ArithmeticException - If x or n is zero, or x is negative and n is even.

ApfloatRuntimeException

root

public Apfloat root(Apfloat x,
 long n)
             throws ArithmeticException,
ApfloatRuntimeException

Root.

Parameters:

x - The operand.

n - Which root to take.

Returns:

x1/n.

Throws:

ArithmeticException - If n is zero, or x is negative and n is even.

ApfloatRuntimeException

scale

public Apfloat scale(Apfloat x,
 long scale)
              throws ApfloatRuntimeException

Move the radix point.

Parameters:

x - The operand.

scale - The amount to move the radix point.

Returns:

x * x.radix()scale.

Throws:

ApfloatRuntimeException

mod

public Apfloat mod(Apfloat x,
 Apfloat y)
            throws ApfloatRuntimeException

Modulus.

Parameters:

x - The first operand.

y - The second operand.

Returns:

x % y.

Throws:

ApfloatRuntimeException

ceil

public Apfloat ceil(Apfloat x)
             throws ApfloatRuntimeException

Ceiling function.

Parameters:

x - The operand.

Returns:

The nearest integer greater than or equal to x.

Throws:

ApfloatRuntimeException

floor

public Apfloat floor(Apfloat x)
              throws ApfloatRuntimeException

Floor function.

Parameters:

x - The operand.

Returns:

The nearest integer less than or equal to x.

Throws:

ApfloatRuntimeException

truncate

public Apfloat truncate(Apfloat x)
                 throws ApfloatRuntimeException

Truncate fractional part.

Parameters:

x - The operand.

Returns:

The nearest integer rounded towards zero from x.

Throws:

ApfloatRuntimeException

frac

public Apfloat frac(Apfloat x)
             throws ApfloatRuntimeException

Extract fractional part.

Parameters:

x - The operand.

Returns:

The fractional part of x.

Throws:

ApfloatRuntimeException

Since:

1.7.0

round

@Deprecated
public Apfloat round(Apfloat x,
 RoundingMode roundingMode)
              throws ApfloatRuntimeException

Deprecated.

Use roundToPrecision(Apfloat,RoundingMode).

Round with specified rounding mode.

Parameters:

x - The operand.

roundingMode - The rounding mode.

Returns:

x rounded with the specified rounding mode.

Throws:

ApfloatRuntimeException

Since:

1.7.0

roundToPrecision

public Apfloat roundToPrecision(Apfloat x,
 RoundingMode roundingMode)
                         throws ApfloatRuntimeException

Round to precision with specified rounding mode.

Parameters:

x - The operand.

roundingMode - The rounding mode.

Returns:

x rounded to the precision of this helper with the specified rounding mode.

Throws:

ArithmeticException - If rounding is necessary (result is not exact) and rounding mode is RoundingMode.UNNECESSARY.

ApfloatRuntimeException

Since:

1.11.0

roundToInteger

public Apfloat roundToInteger(Apfloat x,
 RoundingMode roundingMode)
                       throws ApfloatRuntimeException,
ArithmeticException

Round to integer with specified rounding mode.

Parameters:

x - The operand.

roundingMode - The rounding mode.

Returns:

x rounded to integer with the specified rounding mode.

Throws:

ArithmeticException - If rounding is necessary (result is not exact) and rounding mode is RoundingMode.UNNECESSARY.

ApfloatRuntimeException

Since:

1.11.0

roundToPlaces

public Apfloat roundToPlaces(Apfloat x,
 long places,
 RoundingMode roundingMode)
                      throws ApfloatRuntimeException,
ArithmeticException

Round to specified number of places with specified rounding mode.

Parameters:

x - The operand.

places - The number of places.

roundingMode - The rounding mode.

Returns:

x rounded to the specified number of places with the specified rounding mode.

Throws:

ArithmeticException - If rounding is necessary (result is not exact) and rounding mode is RoundingMode.UNNECESSARY.

ApfloatRuntimeException

Since:

1.11.0

roundToMultiple

public Apfloat roundToMultiple(Apfloat x,
 Apfloat y,
 RoundingMode roundingMode)
                        throws ApfloatRuntimeException,
ArithmeticException

Round to multiple with specified rounding mode.

Parameters:

x - The number to round.

y - The integer multiple to round to.

roundingMode - The rounding mode.

Returns:

x rounded to the nearest multiple of y with the specified rounding mode.

Throws:

ArithmeticException - If rounding is necessary (result is not exact) and rounding mode is RoundingMode.UNNECESSARY.

ApfloatRuntimeException

Since:

1.11.0

w

public Apfloat w(Apfloat x)
          throws ApfloatRuntimeException

Lambert W function.

Parameters:

x - The operand.

Returns:

W0(x).

Throws:

ApfloatRuntimeException

Since:

1.8.0

toDegrees

public Apfloat toDegrees(Apfloat x)
                  throws ApfloatRuntimeException

Convert radians to degrees.

Parameters:

x - The angle in radians.

Returns:

x converted to degrees.

Throws:

ApfloatRuntimeException

Since:

1.8.0

toRadians

public Apfloat toRadians(Apfloat x)
                  throws ApfloatRuntimeException

Convert degrees to radians.

Parameters:

x - The angle in degrees.

Returns:

x converted to radians.

Throws:

ApfloatRuntimeException

Since:

1.8.0

atan2

public Apfloat atan2(Apfloat x,
 Apfloat y)
              throws ArithmeticException,
ApfloatRuntimeException

Angle of point.

Parameters:

x - The operand.

y - The operand.

Returns:

The angle of the point (y, x).

Throws:

ArithmeticException - If x and y are zero.

ApfloatRuntimeException

copySign

public Apfloat copySign(Apfloat x,
 Apfloat y)
                 throws ApfloatRuntimeException

Copies the sign from one number to another.

Parameters:

x - The number to copy the sign to.

y - The number to copy the sign from.

Returns:

x with the sign of y.

Throws:

ApfloatRuntimeException

fmod

public Apfloat fmod(Apfloat x,
 Apfloat y)
             throws ApfloatRuntimeException

Modulus.

Parameters:

x - The first operand.

y - The second operand.

Returns:

x % y.

Throws:

ApfloatRuntimeException

modf

public Apfloat[] modf(Apfloat x)
               throws ApfloatRuntimeException

Split to integer and fractional parts.

Parameters:

x - The operand.

Returns:

An array of two numbers [i, f] where i is floor(x) and f is x - floor(x).

Throws:

ApfloatRuntimeException

factorial

public Apfloat factorial(long n)
                  throws ApfloatRuntimeException

Factorial.

Parameters:

n - The operand.

Returns:

n!.

Throws:

ApfloatRuntimeException

factorial

public Apfloat factorial(long n,
 int radix)
                  throws ApfloatRuntimeException

Factorial.

Parameters:

n - The operand.

radix - The radix of the result.

Returns:

n!.

Throws:

ApfloatRuntimeException

doubleFactorial

public Apfloat doubleFactorial(long n)
                        throws ApfloatRuntimeException

Double factorial.

Parameters:

n - The operand.

Returns:

n!!.

Throws:

ApfloatRuntimeException

Since:

1.14.0

doubleFactorial

public Apfloat doubleFactorial(long n,
 int radix)
                        throws ApfloatRuntimeException

Double factorial.

Parameters:

n - The operand.

radix - The radix of the result.

Returns:

n!!.

Throws:

ApfloatRuntimeException

Since:

1.14.0

pi

public Apfloat pi()
           throws ApfloatRuntimeException

π.

Returns:

π.

Throws:

ApfloatRuntimeException

pi

public Apfloat pi(int radix)
           throws NumberFormatException,
ApfloatRuntimeException

π.

Parameters:

radix - The radix of the result.

Returns:

π.

Throws:

NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

logRadix

public Apfloat logRadix(int radix)
                 throws NumberFormatException,
ApfloatRuntimeException

Logarithm.

Parameters:

radix - The radix of the result.

Returns:

log(radix).

Throws:

NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

multiplyAdd

public Apfloat multiplyAdd(Apfloat a,
 Apfloat b,
 Apfloat c,
 Apfloat d)
                    throws ApfloatRuntimeException

Fused multiply-add.

Parameters:

a - The first operand.

b - The second operand.

c - The third operand.

d - The fourth operand.

Returns:

a * b + c * d.

Throws:

ApfloatRuntimeException

multiplySubtract

public Apfloat multiplySubtract(Apfloat a,
 Apfloat b,
 Apfloat c,
 Apfloat d)
                         throws ApfloatRuntimeException

Fused multiply-subtract.

Parameters:

a - The first operand.

b - The second operand.

c - The third operand.

d - The fourth operand.

Returns:

a * b - c * d.

Throws:

ApfloatRuntimeException

product

public Apfloat product(Apfloat... x)
                throws ApfloatRuntimeException

Product.

Parameters:

x - The operand(s).

Returns:

The product of the operands.

Throws:

ApfloatRuntimeException

sum

public Apfloat sum(Apfloat... x)
            throws ApfloatRuntimeException

Sum.

Parameters:

x - The operand(s).

Returns:

The sum of the operands.

Throws:

ApfloatRuntimeException

gamma

public Apfloat gamma(Apfloat x)
              throws ArithmeticException,
ApfloatRuntimeException

Gamma function.

Parameters:

x - The operand.

Returns:

Γ(x).

Throws:

ArithmeticException - If x is a nonpositive integer.

ApfloatRuntimeException

Since:

1.9.0

gamma

public Apfloat gamma(Apfloat a,
 Apfloat x)
              throws ArithmeticException,
ApfloatRuntimeException

Incomplete gamma function.

Parameters:

a - The first operand.

x - The second operand.

Returns:

Γ(a, x).

Throws:

ArithmeticException - If a is not a positive integer and x is nonpositive.

ApfloatRuntimeException

Since:

1.10.0

gamma

public Apfloat gamma(Apfloat a,
 Apfloat x0,
 Apfloat x1)
              throws ArithmeticException,
ApfloatRuntimeException

Generalized incomplete gamma function.

Parameters:

a - The first operand.

x0 - The second operand.

x1 - The third operand.

Returns:

Γ(a, x0) - Γ(a, x1).

Throws:

ArithmeticException - If a is not a positive integer and either x0 or x1 is nonpositive.

ApfloatRuntimeException

Since:

1.10.0

logGamma

public Apfloat logGamma(Apfloat x)
                 throws ArithmeticException,
ApfloatRuntimeException

Logarithm of the gamma function.

Parameters:

x - The argument.

Returns:

logΓ(x)

Throws:

ArithmeticException - If x is nonpositive.

ApfloatRuntimeException

Since:

1.11.0

digamma

public Apfloat digamma(Apfloat x)
                throws ArithmeticException,
ApfloatRuntimeException

Digamma function.

Parameters:

x - The argument.

Returns:

ψ(x)

Throws:

ArithmeticException - If x is a nonpositive integer.

ApfloatRuntimeException

Since:

1.11.0

polygamma

public Apfloat polygamma(long n,
 Apfloat x)
                  throws ArithmeticException,
ApfloatRuntimeException

Polygamma function.

Parameters:

n - The order.

x - The argument.

Returns:

ψ(n)(x)

Throws:

ArithmeticException - If n is negative or x is a nonpositive integer.

ApfloatRuntimeException

Since:

1.13.0

beta

public Apfloat beta(Apfloat a,
 Apfloat b)
             throws ArithmeticException,
ApfloatRuntimeException

Beta function.

Parameters:

a - The first argument.

b - The second argument.

Returns:

B(a, b)

Throws:

ArithmeticException - If a or b is a nonpositive integer but a + b is not. Also if both a and b are nonpositive integers.

ApfloatRuntimeException

Since:

1.13.0

beta

public Apfloat beta(Apfloat x,
 Apfloat a,
 Apfloat b)
             throws ArithmeticException,
ApfloatRuntimeException

Incomplete beta function.

Parameters:

x - The first argument.

a - The second argument.

b - The third argument.

Returns:

B_x(a, b)

Throws:

ArithmeticException - If a is a nonpositive integer or x is zero and a is nonpositive or x is negative and a is not an integer. Also if x > 1 and the result is not a polynomial.

ApfloatRuntimeException

Since:

1.13.0

beta

public Apfloat beta(Apfloat x1,
 Apfloat x2,
 Apfloat a,
 Apfloat b)
             throws ArithmeticException,
ApfloatRuntimeException

Generalized incomplete beta function.

Parameters:

x1 - The first argument.

x2 - The second argument.

a - The third argument.

b - The fourth argument.

Returns:

B_{(x1, x2)}(a, b)

Throws:

ArithmeticException - If a is a nonpositive integer or x1 or x2 is zero and a is nonpositive or x1 or x2 is negative and a is not an integer. Also if x1 > 1 or x2 > 1 and the result is not a polynomial.

ApfloatRuntimeException

Since:

1.13.0

pochhammer

public Apfloat pochhammer(Apfloat x,
 Apfloat n)
                   throws ArithmeticException,
ApfloatRuntimeException

Pochhammer symbol.

Parameters:

x - The first argument.

n - The second argument.

Returns:

(x)n

Throws:

ArithmeticException - If x + n is a nonpositive integer but x is not.

ApfloatRuntimeException

Since:

1.13.0

binomial

public Apfloat binomial(Apfloat n,
 Apfloat k)
                 throws ArithmeticException,
ApfloatRuntimeException

Binomial coefficient.

Parameters:

n - The argument.

k - The argument.

Returns:

The binomial coefficient.

Throws:

ArithmeticException - If n, k or n - k is a nonpositive integer.

ApfloatRuntimeException

Since:

1.11.0

zeta

public Apfloat zeta(Apfloat s)
             throws ArithmeticException,
ApfloatRuntimeException

Riemann zeta function.

Parameters:

s - The argument.

Returns:

ζ(s)

Throws:

ArithmeticException - If s is 1.

ApfloatRuntimeException

Since:

1.11.0

zeta

public Apfloat zeta(Apfloat s,
 Apfloat a)
             throws ArithmeticException,
ApfloatRuntimeException

Hurwitz zeta function.

Parameters:

s - The first argument.

a - The second argument.

Returns:

ζ(s, a)

Throws:

ArithmeticException - If s is 1 or if a is a nonpositive integer or if s is not an integer and a is nonpositive.

ApfloatRuntimeException

Since:

1.11.0

hypergeometric0F1

public Apfloat hypergeometric0F1(Apfloat a,
 Apfloat x)
                          throws ArithmeticException,
ApfloatRuntimeException

Confluent hypergeometric function ₀F₁.

Parameters:

a - The first argument.

x - The second argument.

Returns:

₀F₁(; a; x)

Throws:

ArithmeticException - If the function value is not finite.

ApfloatRuntimeException

Since:

1.11.0

hypergeometric0F1Regularized

public Apfloat hypergeometric0F1Regularized(Apfloat a,
 Apfloat x)
                                     throws ApfloatRuntimeException

Regularized confluent hypergeometric function ₀F̃₁.

Parameters:

a - The first argument.

x - The second argument.

Returns:

₀F̃₁(; a; x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

hypergeometric1F1

public Apfloat hypergeometric1F1(Apfloat a,
 Apfloat b,
 Apfloat x)
                          throws ArithmeticException,
ApfloatRuntimeException

Kummer confluent hypergeometric function ₁F₁.

Parameters:

a - The first argument.

b - The second argument.

x - The third argument.

Returns:

₁F₁(a; b; x)

Throws:

ArithmeticException - If the function value is not finite.

ApfloatRuntimeException

Since:

1.11.0

hypergeometric1F1Regularized

public Apfloat hypergeometric1F1Regularized(Apfloat a,
 Apfloat b,
 Apfloat x)
                                     throws ApfloatRuntimeException

Regularized Kummer confluent hypergeometric function ₁F̃₁.

Parameters:

a - The first argument.

b - The second argument.

x - The third argument.

Returns:

₁F̃₁(a; b; x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

hypergeometric2F1

public Apfloat hypergeometric2F1(Apfloat a,
 Apfloat b,
 Apfloat c,
 Apfloat x)
                          throws ArithmeticException,
ApfloatRuntimeException

Hypergeometric function ₂F₁.

Parameters:

a - The first argument.

b - The second argument.

c - The third argument.

x - The fourth argument.

Returns:

₂F₁(a, b; c; x)

Throws:

ArithmeticException - If the function value is not finite or real.

ApfloatRuntimeException

Since:

1.11.0

hypergeometric2F1Regularized

public Apfloat hypergeometric2F1Regularized(Apfloat a,
 Apfloat b,
 Apfloat c,
 Apfloat x)
                                     throws ApfloatRuntimeException

Regularized hypergeometric function ₂F̃₁.

Parameters:

a - The first argument.

b - The second argument.

c - The third argument.

x - The fourth argument.

Returns:

₂F̃₁(a, b; c; x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

hypergeometricU

public Apfloat hypergeometricU(Apfloat a,
 Apfloat b,
 Apfloat x)
                        throws ArithmeticException,
ApfloatRuntimeException

Tricomi's confluent hypergeometric function U.

Parameters:

a - The first argument.

b - The second argument.

x - The third argument.

Returns:

U(a, b, x)

Throws:

ArithmeticException - If the result would be complex or not finite.

ApfloatRuntimeException

Since:

1.13.0

erf

public Apfloat erf(Apfloat x)
            throws ApfloatRuntimeException

Error function.

Parameters:

x - The argument.

Returns:

erf(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

erfc

public Apfloat erfc(Apfloat x)
             throws ApfloatRuntimeException

Complementary error function.

Parameters:

x - The argument.

Returns:

erfc(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

erfi

public Apfloat erfi(Apfloat x)
             throws ApfloatRuntimeException

Imaginary error function.

Parameters:

x - The argument.

Returns:

erfi(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

inverseErf

public Apfloat inverseErf(Apfloat x)
                   throws ArithmeticException,
ApfloatRuntimeException

Inverse error function.

Parameters:

x - The argument.

Returns:

erf⁻¹(x)

Throws:

ArithmeticException - If |x| is ≥ 1.

ApfloatRuntimeException

Since:

1.13.0

inverseErfc

public Apfloat inverseErfc(Apfloat x)
                    throws ArithmeticException,
ApfloatRuntimeException

Inverse complementary error function.

Parameters:

x - The argument.

Returns:

erfc⁻¹(x)

Throws:

ArithmeticException - If x is ≤ 0 or ≥ 2.

ApfloatRuntimeException

Since:

1.13.0

fresnelS

public Apfloat fresnelS(Apfloat x)
                 throws ApfloatRuntimeException

Fresnel integral S.

Parameters:

x - The argument.

Returns:

S(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

fresnelC

public Apfloat fresnelC(Apfloat x)
                 throws ApfloatRuntimeException

Fresnel integral C.

Parameters:

x - The argument.

Returns:

C(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

expIntegralE

public Apfloat expIntegralE(Apfloat ν,
 Apfloat x)
                     throws ArithmeticException,
ApfloatRuntimeException

Exponential integral E.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

E_ν(x)

Throws:

ArithmeticException - If ν is < 0 and x is zero or ν is nonzero and x is negative.

ApfloatRuntimeException

Since:

1.13.0

expIntegralEi

public Apfloat expIntegralEi(Apfloat x)
                      throws ArithmeticException,
ApfloatRuntimeException

Exponential integral Ei.

Parameters:

x - The argument.

Returns:

Ei(x)

Throws:

ArithmeticException - If x is zero.

ApfloatRuntimeException

Since:

1.13.0

logIntegral

public Apfloat logIntegral(Apfloat x)
                    throws ArithmeticException,
ApfloatRuntimeException

Logarithmic integral.

Parameters:

x - The argument.

Returns:

li(x)

Throws:

ArithmeticException - If x is nonpositive or 1.

ApfloatRuntimeException

Since:

1.13.0

sinIntegral

public Apfloat sinIntegral(Apfloat x)
                    throws ApfloatRuntimeException

Sine integral.

Parameters:

x - The argument.

Returns:

Si(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

cosIntegral

public Apfloat cosIntegral(Apfloat x)
                    throws ArithmeticException,
ApfloatRuntimeException

Cosine integral.

Parameters:

x - The argument.

Returns:

Ci(x)

Throws:

ArithmeticException - If x is nonpositive.

ApfloatRuntimeException

Since:

1.13.0

sinhIntegral

public Apfloat sinhIntegral(Apfloat x)
                     throws ApfloatRuntimeException

Hyperbolic sine integral.

Parameters:

x - The argument.

Returns:

Shi(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

coshIntegral

public Apfloat coshIntegral(Apfloat x)
                     throws ArithmeticException,
ApfloatRuntimeException

Hyperbolic cosine integral.

Parameters:

x - The argument.

Returns:

Chi(x)

Throws:

ArithmeticException - If x is nonpositive.

ApfloatRuntimeException

Since:

1.13.0

airyAi

public Apfloat airyAi(Apfloat x)
               throws ApfloatRuntimeException

Airy function Ai.

Parameters:

x - The argument.

Returns:

Ai(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

airyAiPrime

public Apfloat airyAiPrime(Apfloat x)
                    throws ApfloatRuntimeException

Derivative of the Airy function Ai.

Parameters:

x - The argument.

Returns:

Ai′(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

airyBi

public Apfloat airyBi(Apfloat x)
               throws ApfloatRuntimeException

Airy function Bi.

Parameters:

x - The argument.

Returns:

Bi(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

airyBiPrime

public Apfloat airyBiPrime(Apfloat x)
                    throws ApfloatRuntimeException

Derivative of the Airy function Bi.

Parameters:

x - The argument.

Returns:

Bi′(x)

Throws:

ApfloatRuntimeException

Since:

1.13.0

besselJ

public Apfloat besselJ(Apfloat ν,
 Apfloat x)
                throws ArithmeticException,
ApfloatRuntimeException

Bessel function of the first kind.

Parameters:

ν - The order.

x - The argument.

Returns:

J_ν(x)

Throws:

ArithmeticException - If ν is < 0 and ν is not an integer and x is zero. Also if ν is not an integer and x is < 0.

ApfloatRuntimeException

Since:

1.13.0

besselI

public Apfloat besselI(Apfloat ν,
 Apfloat x)
                throws ArithmeticException,
ApfloatRuntimeException

Modified Bessel function of the first kind.

Parameters:

ν - The order.

x - The argument.

Returns:

I_ν(x)

Throws:

ArithmeticException - If ν is < 0 and ν is not an integer and x is zero. Also if ν is not an integer and x is < 0.

ApfloatRuntimeException

Since:

1.13.0

besselY

public Apfloat besselY(Apfloat ν,
 Apfloat x)
                throws ArithmeticException,
ApfloatRuntimeException

Bessel function of the second kind.

Parameters:

ν - The order.

x - The argument.

Returns:

Y_ν(x)

Throws:

ArithmeticException - If x is ≤ 0.

ApfloatRuntimeException

Since:

1.13.0

besselK

public Apfloat besselK(Apfloat ν,
 Apfloat x)
                throws ArithmeticException,
ApfloatRuntimeException

Modified Bessel function of the second kind.

Parameters:

ν - The order.

x - The argument.

Returns:

K_ν(x)

Throws:

ArithmeticException - If x is ≤ 0.

ApfloatRuntimeException

Since:

1.13.0

ellipticK

public Apfloat ellipticK(Apfloat x)
                  throws ArithmeticException,
ApfloatRuntimeException

Complete elliptic integral of the first kind.

Parameters:

x - The argument.

Returns:

K(x)

Throws:

ArithmeticException - If x is ≥ 1.

ApfloatRuntimeException

Since:

1.13.0

ellipticE

public Apfloat ellipticE(Apfloat x)
                  throws ArithmeticException,
ApfloatRuntimeException

Complete elliptic integral of the second kind.

Parameters:

x - The argument.

Returns:

E(x)

Throws:

ArithmeticException - If x is > 1.

ApfloatRuntimeException

Since:

1.13.0

hermiteH

public Apfloat hermiteH(Apfloat ν,
 Apfloat x)
                 throws ApfloatRuntimeException

Hermite function.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

H_ν(x)

Throws:

ApfloatRuntimeException

Since:

1.14.0

laguerreL

public Apfloat laguerreL(Apfloat ν,
 Apfloat x)
                  throws ApfloatRuntimeException

Laguerre function.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

L_ν(x)

Throws:

ApfloatRuntimeException

Since:

1.14.0

laguerreL

public Apfloat laguerreL(Apfloat ν,
 Apfloat λ,
 Apfloat x)
                  throws ApfloatRuntimeException

Generalized Laguerre function.

Parameters:

ν - The first argument.

λ - The second argument.

x - The third argument.

Returns:

L_ν^λ(x)

Throws:

ApfloatRuntimeException

Since:

1.14.0

legendreP

public Apfloat legendreP(Apfloat ν,
 Apfloat x)
                  throws ArithmeticException,
ApfloatRuntimeException

Legendre function.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

P_ν(x)

Throws:

ArithmeticException - If ν is not an integer and x ≤ -1.

ApfloatRuntimeException

Since:

1.14.0

legendreP

public Apfloat legendreP(Apfloat ν,
 Apfloat μ,
 Apfloat x)
                  throws ArithmeticException,
ApfloatRuntimeException

Associated Legendre function of the first kind.

Parameters:

ν - The first argument.

μ - The second argument.

x - The third argument.

Returns:

P_ν^μ(x)

Throws:

ArithmeticException - If x is ≤ -1 or ≥ 1 and ν or μ is not an integer or μ is not even or μ is not positive and -μ ≤ ν < μ.

ApfloatRuntimeException

Since:

1.14.0

legendreQ

public Apfloat legendreQ(Apfloat ν,
 Apfloat x)
                  throws ArithmeticException,
ApfloatRuntimeException

Legendre function of the second kind.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

Q_ν(x)

Throws:

ArithmeticException - If x is ≥ 1 or ≤ -1.

ApfloatRuntimeException

Since:

1.14.0

legendreQ

public Apfloat legendreQ(Apfloat ν,
 Apfloat μ,
 Apfloat x)
                  throws ArithmeticException,
ApfloatRuntimeException

Associated Legendre function of the second kind.

Parameters:

ν - The first argument.

μ - The second argument.

x - The third argument.

Returns:

Q_ν^μ(x)

Throws:

ArithmeticException - If x is ≥ 1 or ≤ -1.

ApfloatRuntimeException

Since:

1.14.0

chebyshevT

public Apfloat chebyshevT(Apfloat ν,
 Apfloat x)
                   throws ArithmeticException,
ApfloatRuntimeException

Chebyshev function of the first kind.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

T_ν(x)

Throws:

ArithmeticException - If x is < -1 and ν is not an integer.

ApfloatRuntimeException

Since:

1.14.0

chebyshevU

public Apfloat chebyshevU(Apfloat ν,
 Apfloat x)
                   throws ArithmeticException,
ApfloatRuntimeException

Chebyshev function of the second kind.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

U_ν(x)

Throws:

ArithmeticException - If x is ≤ -1 and ν is not an integer.

ApfloatRuntimeException

Since:

1.14.0

gegenbauerC

public Apfloat gegenbauerC(Apfloat ν,
 Apfloat x)
                    throws ArithmeticException,
ApfloatRuntimeException

Renormalized Gegenbauer function.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

C_ν⁽⁰⁾(x)

Throws:

ArithmeticException - If ν is zero. Also if x is < -1 and ν is not an integer.

ApfloatRuntimeException

Since:

1.14.0

gegenbauerC

public Apfloat gegenbauerC(Apfloat ν,
 Apfloat λ,
 Apfloat x)
                    throws ArithmeticException,
ApfloatRuntimeException

Gegenbauer function.

Parameters:

ν - The first argument.

λ - The second argument.

x - The third argument.

Returns:

C_ν^λ(x)

Throws:

ArithmeticException - If x is < -1 and ν is not an integer. Also if x is -1 and λ is > 1/2. Also if x is -1 and λ is 1/2 and ν is not an integer.

ApfloatRuntimeException

Since:

1.14.0

jacobiP

public Apfloat jacobiP(Apfloat ν,
 Apfloat a,
 Apfloat b,
 Apfloat x)
                throws ArithmeticException,
ApfloatRuntimeException

Jacobi function.

Parameters:

ν - The first argument.

a - The second argument.

b - The third argument.

x - The fourth argument.

Returns:

P_ν^(a,b)(x)

Throws:

ArithmeticException - If ν is not a positive integer and either x is -1 and b is > 0 or x is < -1. Also if ν + a is a negative integer and ν is not an integer.

ApfloatRuntimeException

Since:

1.14.0

fibonacci

public Apfloat fibonacci(Apfloat ν,
 Apfloat x)
                  throws ApfloatRuntimeException

Fibonacci function.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

F_ν(x)

Throws:

ApfloatRuntimeException

Since:

1.14.0

eulerE

public Apfloat eulerE(long n,
 Apfloat x)
               throws IllegalArgumentException,
ApfloatRuntimeException

Euler polynomial.

Parameters:

n - The first argument.

x - The second argument.

Returns:

E_n(x)

Throws:

IllegalArgumentException - If n < 0.

ApfloatRuntimeException

Since:

1.14.0

bernoulliB

public Apfloat bernoulliB(long n,
 Apfloat x)
                   throws IllegalArgumentException,
ApfloatRuntimeException

Bernoulli polynomial.

Parameters:

n - The first argument.

x - The second argument.

Returns:

B_n(x)

Throws:

IllegalArgumentException - If n < 0.

ApfloatRuntimeException

Since:

1.14.0

harmonicNumber

public Apfloat harmonicNumber(Apfloat x)
                       throws ArithmeticException,
ApfloatRuntimeException

Harmonic number.

Parameters:

x - The argument.

Returns:

H_x

Throws:

ArithmeticException - If x is a negative integer.

ApfloatRuntimeException

Since:

1.14.0

harmonicNumber

public Apfloat harmonicNumber(Apfloat x,
 Apfloat r)
                       throws ArithmeticException,
ApfloatRuntimeException

Generalized harmonic number.

Parameters:

x - The first argument.

r - The second argument.

Returns:

H_x^(r)

Throws:

ArithmeticException - If x is a negative integer, unless r is a nonpositive integer. Also if x is < -1 and r is not an integer.

ApfloatRuntimeException

Since:

1.14.0

polylog

public Apfloat polylog(Apfloat ν,
 Apfloat x)
                throws ArithmeticException,
ApfloatRuntimeException

Polylogarithm.

Parameters:

ν - The first argument.

x - The second argument.

Returns:

Li_ν(x)

Throws:

ArithmeticException - If ν is ≤ 1 and x is 1 or if x is > 1.

ApfloatRuntimeException

Since:

1.14.0

logisticSigmoid

public Apfloat logisticSigmoid(Apfloat x)
                        throws ApfloatRuntimeException

Logistic sigmoid.

Parameters:

x - The argument.

Returns:

σ(x)

Throws:

ApfloatRuntimeException

Since:

1.14.0

random

public Apfloat random()
               throws ApfloatRuntimeException

Return a uniformly distributed random number 0 ≤ x < 1.

Returns:

A random number.

Throws:

ApfloatRuntimeException

Since:

1.9.0

random

public Apfloat random(int radix)
               throws NumberFormatException,
ApfloatRuntimeException

Return a uniformly distributed random number 0 ≤ x < 1.

Parameters:

radix - The radix of the number.

Returns:

A random number.

Throws:

NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

Since:

1.9.0

randomGaussian

public Apfloat randomGaussian()
                       throws ApfloatRuntimeException

Return a normally distributed random number with mean 0 and standard deviation 1.

Returns:

A random number.

Throws:

ApfloatRuntimeException

Since:

1.9.0

randomGaussian

public Apfloat randomGaussian(int radix)
                       throws NumberFormatException,
ApfloatRuntimeException

Return a normally distributed random number with mean 0 and standard deviation 1.

Parameters:

radix - The radix of the number.

Returns:

A random number.

Throws:

NumberFormatException - If the radix is invalid.

ApfloatRuntimeException

Since:

1.9.0

continuedFraction

public Apfloat[] continuedFraction(Apfloat x,
 int n)
                            throws ApfloatRuntimeException

Continued fraction.

Parameters:

x - The value.

n - Maximum number of terms.

Returns:

The continued fraction.

Throws:

IllegalArgumentException - If n is less than one.

ApfloatRuntimeException

Since:

1.12.0

convergents

public Apfloat[] convergents(Apfloat x,
 int n)
                      throws ApfloatRuntimeException

Convergents.

Parameters:

x - The value.

n - Maximum number of convergents.

Returns:

The convergents.

Throws:

IllegalArgumentException - If n is less than one.

ApfloatRuntimeException

Since:

1.12.0

max

public Apfloat max(Apfloat x,
 Apfloat y)
            throws ApfloatRuntimeException

Maximum value.

Parameters:

x - The first operand.

y - The second operand.

Returns:

The maximum of x and y.

Throws:

ApfloatRuntimeException

Since:

1.9.0

min

public Apfloat min(Apfloat x,
 Apfloat y)
            throws ApfloatRuntimeException

Minimum value.

Parameters:

x - The first operand.

y - The second operand.

Returns:

The minimum of x and y.

Throws:

ApfloatRuntimeException

Since:

1.9.0

nextAfter

public Apfloat nextAfter(Apfloat x,
 Apfloat y)
                  throws ApfloatRuntimeException

The number adjacent to the first argument in the direction of the second argument.

Parameters:

x - The first operand.

y - The second operand.

Returns:

The number adjacent to the first argument in the direction of the second argument.

Throws:

ApfloatRuntimeException

Since:

1.10.0

nextDown

public Apfloat nextDown(Apfloat x)
                 throws ApfloatRuntimeException

The adjacent value closer to negative infinity.

Parameters:

x - The operand.

Returns:

The adjacent value closer to negative infinity.

Throws:

ApfloatRuntimeException

Since:

1.10.0

nextUp

public Apfloat nextUp(Apfloat x)
               throws ApfloatRuntimeException

The adjacent value closer to positive infinity.

Parameters:

x - The operand.

Returns:

The adjacent value closer to positive infinity.

Throws:

ApfloatRuntimeException

Since:

1.10.0

ulp

public Apfloat ulp(Apfloat x)
            throws ApfloatRuntimeException

Unit in the last place.

Parameters:

x - The operand.

Returns:

The unit in the last place.

Throws:

ApfloatRuntimeException

Since:

1.10.0