TYoshimura.DoubleDouble 4.2.6

.NET 8.0

dotnet add package TYoshimura.DoubleDouble --version 4.2.6

NuGet\Install-Package TYoshimura.DoubleDouble -Version 4.2.6

This command is intended to be used within the Package Manager Console in Visual Studio, as it uses the NuGet module's version of Install-Package.

<PackageReference Include="TYoshimura.DoubleDouble" Version="4.2.6" />

For projects that support PackageReference, copy this XML node into the project file to reference the package.

<PackageVersion Include="TYoshimura.DoubleDouble" Version="4.2.6" />
                    

                            Directory.Packages.props

<PackageReference Include="TYoshimura.DoubleDouble" />
                    

                            Project file

For projects that support Central Package Management (CPM), copy this XML node into the solution Directory.Packages.props file to version the package.

paket add TYoshimura.DoubleDouble --version 4.2.6

The NuGet Team does not provide support for this client. Please contact its maintainers for support.

#r "nuget: TYoshimura.DoubleDouble, 4.2.6"

#r directive can be used in F# Interactive and Polyglot Notebooks. Copy this into the interactive tool or source code of the script to reference the package.

#addin nuget:?package=TYoshimura.DoubleDouble&version=4.2.6
                    

                            Install TYoshimura.DoubleDouble as a Cake Addin

#tool nuget:?package=TYoshimura.DoubleDouble&version=4.2.6
                    

                            Install TYoshimura.DoubleDouble as a Cake Tool

The NuGet Team does not provide support for this client. Please contact its maintainers for support.

DoubleDouble

Double-Double Arithmetic and Special Function Implements

Requirement

.NET 8.0

Install

Download DLL
Download Nuget

More Precision ?

MultiPrecision

Type

type	mantissa bits	significant digits
ddouble	106	31

limit	bin	dec
MaxValue	2^1024	1.79769e308
Normal MinValue	2^-968	4.00833e-292
Subnormal MinValue	2^-1074	4.94066e-324

Functions

function	domain	mantissa error bits	note
ddouble.Sqrt(x)	[0,+inf)	2
ddouble.Cbrt(x)	(-inf,+inf)	2
ddouble.RootN(x, n)	(-inf,+inf)	3
ddouble.Log2(x)	(0,+inf)	2
ddouble.Log(x)	(0,+inf)	3
ddouble.Log(x, b)	(0,+inf)	3
ddouble.Log10(x)	(0,+inf)	3
ddouble.Log1p(x)	(-1,+inf)	3	log(1+x)
ddouble.Pow2(x)	(-inf,+inf)	1
ddouble.Pow2m1(x)	(-inf,+inf)	2	pow2(x)-1
ddouble.Pow(x, y)	(-inf,+inf)	2
ddouble.Pow1p(x, y)	(-inf,+inf)	2	pow(1+x, y)
ddouble.Pow10(x)	(-inf,+inf)	2
ddouble.Exp(x)	(-inf,+inf)	2
ddouble.Expm1(x)	(-inf,+inf)	2	exp(x)-1
ddouble.Sin(x)	(-inf,+inf)	2
ddouble.Cos(x)	(-inf,+inf)	2
ddouble.Tan(x)	(-inf,+inf)	3
ddouble.SinPi(x)	(-inf,+inf)	1	sin(πx)
ddouble.CosPi(x)	(-inf,+inf)	1	cos(πx)
ddouble.TanPi(x)	(-inf,+inf)	2	tan(πx)
ddouble.Sinh(x)	(-inf,+inf)	2
ddouble.Cosh(x)	(-inf,+inf)	2
ddouble.Tanh(x)	(-inf,+inf)	2
ddouble.Asin(x)	[-1,1]	2	Accuracy deteriorates near x=-1,1.
ddouble.Acos(x)	[-1,1]	2	Accuracy deteriorates near x=-1,1.
ddouble.Atan(x)	(-inf,+inf)	2
ddouble.Atan2(y, x)	(-inf,+inf)	2
ddouble.AsinPi(x)	[-1,1]	3	Accuracy deteriorates near x=-1,1.
ddouble.AcosPi(x)	[-1,1]	3	Accuracy deteriorates near x=-1,1.
ddouble.AtanPi(x)	(-inf,+inf)	3
ddouble.Atan2Pi(y, x)	(-inf,+inf)	3
ddouble.Asinh(x)	(-inf,+inf)	2
ddouble.Acosh(x)	[1,+inf)	2
ddouble.Atanh(x)	(-1,1)	4	Accuracy deteriorates near x=-1,1.
ddouble.Sinc(x, normalized)	(-inf,+inf)	2	normalized: x → πx
ddouble.Sinhc(x)	(-inf,+inf)	3
ddouble.Gamma(x)	(-inf,+inf)	2	Accuracy deteriorates near non-positive intergers. If x is Natual number lass than 35, an exact integer value is returned.
ddouble.LogGamma(x)	(0,+inf)	4
ddouble.Digamma(x)	(-inf,+inf)	4	Near the positive root, polynomial interpolation is used.
ddouble.Polygamma(n, x)	(-inf,+inf)	4	Accuracy deteriorates near non-positive intergers. n ≤ 16
ddouble.InverseGamma(x)	[sqrt(π)/2,+inf)	2	gamma^-1(x)
ddouble.InverseDigamma(x)	(-inf,+inf)	2	digamma^-1(x)
ddouble.RcpGamma(x)	(-inf,+inf)	3	1/gamma(x)
ddouble.LowerIncompleteGamma(nu, x)	[0,+inf)	4	nu ≤ 171.625
ddouble.UpperIncompleteGamma(nu, x)	[0,+inf)	4	nu ≤ 171.625
ddouble.LowerIncompleteGammaRegularized(nu, x)	[0,+inf)	4	nu ≤ 8192
ddouble.UpperIncompleteGammaRegularized(nu, x)	[0,+inf)	4	nu ≤ 8192
ddouble.InverseLowerIncompleteGamma(nu, x)	[0,1]	8	nu ≤ 8192
ddouble.InverseUpperIncompleteGamma(nu, x)	[0,1]	8	nu ≤ 8192
ddouble.Beta(a, b)	[0,+inf)	4
ddouble.LogBeta(a, b)	[0,+inf)	4
ddouble.IncompleteBeta(x, a, b)	[0,1]	4	Accuracy decreases when the radio of a,b is too large. a+b-max(a,b) ≤ 512
ddouble.IncompleteBetaRegularized(x, a, b)	[0,1]	4	Accuracy decreases when the radio of a,b is too large. a+b-max(a,b) ≤ 8192
ddouble.InverseIncompleteBeta(x, a, b)	[0,1]	8	Accuracy decreases when the radio of a,b is too large. a+b-max(a,b) ≤ 8192
ddouble.Erf(x)	(-inf,+inf)	3
ddouble.Erfc(x)	(-inf,+inf)	3
ddouble.InverseErf(x)	(-1,1)	3
ddouble.InverseErfc(x)	(0,2)	3
ddouble.Erfcx(x)	(-inf,+inf)	3
ddouble.Erfi(x)	(-inf,+inf)	4
ddouble.DawsonF(x)	(-inf,+inf)	4
ddouble.BesselJ(nu, x)	[0,+inf)	6	Accuracy deteriorates near root. abs(nu) ≤ 256
ddouble.BesselY(nu, x)	[0,+inf)	6	Accuracy deteriorates near root. abs(nu) ≤ 256
ddouble.BesselI(nu, x)	[0,+inf)	6	Accuracy deteriorates near root. abs(nu) ≤ 256
ddouble.BesselK(nu, x)	[0,+inf)	6	abs(nu) ≤ 256
ddouble.StruveH(n, x)	(-inf,+inf)	4	0 ≤ n ≤ 8
ddouble.StruveK(n, x)	[0,+inf)	4	0 ≤ n ≤ 8
ddouble.StruveL(n, x)	(-inf,+inf)	4	0 ≤ n ≤ 8
ddouble.StruveM(n, x)	[0,+inf)	4	0 ≤ n ≤ 8
ddouble.AngerJ(n, x)	(-inf,+inf)	6
ddouble.WeberE(n, x)	(-inf,+inf)	6	0 ≤ n ≤ 8
ddouble.Jinc(x)	(-inf,+inf)	3
ddouble.EllipticK(m)	[0,1]	4	k: elliptic modulus, m=k^2
ddouble.EllipticE(m)	[0,1]	4	k: elliptic modulus, m=k^2
ddouble.EllipticPi(n, m)	[0,1]	4	k: elliptic modulus, m=k^2
ddouble.EllipticK(x, m)	[0,2π]	4	k: elliptic modulus, m=k^2
ddouble.EllipticE(x, m)	[0,2π]	4	k: elliptic modulus, m=k^2, incomplete elliptic integral
ddouble.EllipticPi(n, x, m)	[0,2π]	4	k: elliptic modulus, m=k^2 Argument order follows wolfram. incomplete elliptic integral
ddouble.EllipticTheta(a, x, q)	(-inf,+inf)	4	incomplete elliptic integral, a=1...4, q ≤ 0.995
ddouble.KeplerE(m, e, centered)	(-inf,+inf)	6	inverse kepler's equation, e(eccentricity) ≤ 256
ddouble.Agm(a, b)	[0,+inf)	2
ddouble.FresnelC(x)	(-inf,+inf)	4
ddouble.FresnelS(x)	(-inf,+inf)	4
ddouble.FresnelF(x)	(-inf,+inf)	4
ddouble.FresnelG(x)	(-inf,+inf)	4
ddouble.Ei(x)	(-inf,+inf)	4	exponential integral
ddouble.Ein(x)	(-inf,+inf)	4	complementary exponential integral
ddouble.En(n, x)	[0,+inf)	4	exponential integral, n ≤ 256
ddouble.Li(x)	[0,+inf)	5	logarithmic integral li(x)=ei(log(x))
ddouble.Si(x, limit_zero)	(-inf,+inf)	4	sin integral, limit_zero=true: si(x)
ddouble.Ci(x)	[0,+inf)	4	cos integral
ddouble.Ti(x)	(-inf,+inf)	4	arctan integral
ddouble.Shi(x)	(-inf,+inf)	5	hyperbolic sin integral
ddouble.Chi(x)	[0,+inf)	5	hyperbolic cos integral
ddouble.Clausen(x, normalized)	(-inf,+inf)	3	Clausen function of order 2, Cl_2(x), normalized: x → πx
ddouble.BarnesG(x)	(-inf,+inf)	3
ddouble.LogBarnesG(x)	(0,+inf)	3
ddouble.LambertW(x)	[-1/e,+inf)	4
ddouble.AiryAi(x)	(-inf,+inf)	5	Accuracy deteriorates near root.
ddouble.AiryBi(x)	(-inf,+inf)	5	Accuracy deteriorates near root.
ddouble.ScorerGi(x)	(-inf,+inf)	5	Accuracy deteriorates near root.
ddouble.ScorerHi(x)	(-inf,+inf)	4
ddouble.JacobiSn(x, m)	(-inf,+inf)	4	k: elliptic modulus, m=k^2
ddouble.JacobiCn(x, m)	(-inf,+inf)	4	k: elliptic modulus, m=k^2
ddouble.JacobiDn(x, m)	(-inf,+inf)	4	k: elliptic modulus, m=k^2
ddouble.JacobiAm(x, m)	(-inf,+inf)	4	k: elliptic modulus, m=k^2
ddouble.JacobiArcSn(x, m)	[-1,+1]	4	k: elliptic modulus, m=k^2
ddouble.JacobiArcCn(x, m)	[-1,+1]	4	k: elliptic modulus, m=k^2
ddouble.JacobiArcDn(x, m)	[0,1]	4	k: elliptic modulus, m=k^2
ddouble.CarlsonRD(x, y, z)	[0,+inf)	4
ddouble.CarlsonRC(x, y)	[0,+inf)	4
ddouble.CarlsonRF(x, y, z)	[0,+inf)	4
ddouble.CarlsonRJ(x, y, z, rho)	[0,+inf)	4
ddouble.CarlsonRG(x, y, z)	[0,+inf)	4
ddouble.RiemannZeta(x)	(-inf,+inf)	3
ddouble.HurwitzZeta(x, a)	(1,+inf)	3	a ≥ 0
ddouble.DirichletEta(x)	(-inf,+inf)	3
ddouble.Polylog(n, x)	(-inf,1]	3	n ∈ [-4,8]
ddouble.OwenT(h, a)	(-inf,+inf)	5
ddouble.Bump(x)	(-inf,+inf)	4	C-infinity smoothness basis function, bump(x)=1/(exp(1/x-1/(1-x))+1)
ddouble.HermiteH(n, x)	(-inf,+inf)	3	n ≤ 64
ddouble.LaguerreL(n, x)	(-inf,+inf)	3	n ≤ 64
ddouble.LaguerreL(n, alpha, x)	(-inf,+inf)	3	n ≤ 64, associated
ddouble.LegendreP(n, x)	(-inf,+inf)	3	n ≤ 64
ddouble.LegendreP(n, m, x)	[-1,1]	3	n ≤ 64, associated
ddouble.ChebyshevT(n, x)	(-inf,+inf)	3	n ≤ 64
ddouble.ChebyshevU(n, x)	(-inf,+inf)	3	n ≤ 64
ddouble.ZernikeR(n, m, x)	[0,1]	3	n ≤ 64
ddouble.GegenbauerC(n, alpha, x)	(-inf,+inf)	3	n ≤ 64
ddouble.JacobiP(n, alpha, beta, x)	[-1,1]	3	n ≤ 64, alpha,beta > -1
ddouble.Bernoulli(n, x, centered)	[0,1]	4	n ≤ 64, centered: x->x-1/2
ddouble.Cyclotomic(n, x)	(-inf,+inf)	1	n ≤ 32
ddouble.MathieuA(n, q)	(-inf,+inf)	4	n ≤ 16
ddouble.MathieuB(n, q)	(-inf,+inf)	4	n ≤ 16
ddouble.MathieuC(n, q, x)	(-inf,+inf)	4	n ≤ 16, Accuracy deteriorates when q is very large.
ddouble.MathieuS(n, q, x)	(-inf,+inf)	4	n ≤ 16, Accuracy deteriorates when q is very large.
ddouble.EulerQ(q)	(-1,1)	4
ddouble.LogEulerQ(q)	(-1,1)	4
ddouble.Ldexp(x, y)	(-inf,+inf)	N/A
ddouble.Binomial(n, k)	N/A	1	n ≤ 1000
ddouble.Hypot(x, y)	N/A	2
ddouble.GeometricMean(x, y)	N/A	2
ddouble.Logit(x)	(0,1)	2
ddouble.Expit(x)	(-inf,+inf)	2
ddouble.Min(x, y)	N/A	N/A
ddouble.Max(x, y)	N/A	N/A
ddouble.Clamp(v, min, max)	N/A	N/A
ddouble.CopySign(value, sign)	N/A	N/A
ddouble.Floor(x)	N/A	N/A
ddouble.Ceiling(x)	N/A	N/A
ddouble.Round(x)	N/A	N/A
ddouble.Truncate(x)	N/A	N/A
IEnumerable<ddouble>.Sum()	N/A	N/A
IEnumerable<ddouble>.Average()	N/A	N/A
IEnumerable<ddouble>.Min()	N/A	N/A
IEnumerable<ddouble>.Max()	N/A	N/A

Constants

constant	value	note
ddouble.Pi	3.141592653589793238462...	Pi
ddouble.E	2.718281828459045235360...	Napier's E
ddouble.Sqrt2	1.414213562373095048801...	Sqrt(2)
ddouble.GoldenRatio	1.618033988749894848204...	Golden ratio
ddouble.Lg2	0.301029995663981195213...	log10(2)
ddouble.Lb10	3.321928094887362347870...	log2(10)
ddouble.Ln2	0.693147180559945309417...	log(2)
ddouble.LbE	1.442695040888963407359...	log2(e)
ddouble.EulerGamma	0.577215664901532860606...	Euler's Gamma
ddouble.Zeta3	1.202056903159594285399...	ζ(3), Apery const.
ddouble.Zeta5	1.036927755143369926331...	ζ(5)
ddouble.Zeta7	1.008349277381922826839...	ζ(7)
ddouble.Zeta9	1.002008392826082214418...	ζ(9)
ddouble.DigammaZero	1.461632144968362341263...	Positive root of digamma
ddouble.ErdosBorwein	1.606695152415291763783...	Erdös Borwein constant
ddouble.FeigenbaumDelta	4.669201609102990671853...	Feigenbaum constant
ddouble.FeigenbaumAlpha	2.502907875095892822283...	Feigenbaum constant
ddouble.LemniscatePi	2.622057554292119810465...	Lemniscate constant
ddouble.GlaisherA	1.282427129100622636875...	Glaisher–Kinkelin constant
ddouble.CatalanG	0.915965594177219015055...	Catalan's constant
ddouble.FransenRobinson	2.807770242028519365222...	Fransén–Robinson constant
ddouble.KhinchinK	2.685452001065306445310...	Khinchin's constant
ddouble.MeisselMertens	0.261497212847642783755...	Meissel–Mertens constant
ddouble.LambertOmega	0.567143290409783873000...	LambertW(1)
ddouble.LandauRamanujan	0.764223653589220662991...	Landau–Ramanujan constant
ddouble.MillsTheta	1.306377883863080690469...	Mills constant
ddouble.SoldnerMu	1.451369234883381050284...	Ramanujan–Soldner constant
ddouble.SierpinskiK	0.822825249678847032995...	Sierpiński's constant, Define follows wolfram.
ddouble.RcpFibonacci	3.359885666243177553172...	Reciprocal Fibonacci constant
ddouble.Niven	1.705211140105367764289...	Niven's constant
ddouble.GolombDickman	0.624329988543550870992...	Golomb–Dickman constant

Sequence

sequence	note
ddouble.TaylorSequence	Taylor,1/n!
ddouble.Factorial	Factorial,n!
ddouble.BernoulliSequence	Bernoulli,B(2k)
ddouble.HarmonicNumber	HarmonicNumber, H_n
ddouble.StieltjesGamma	StieltjesGamma, γ_n

Casts

long (accurately)

ddouble v0 = 123;
long n0 = (long)v0;

double (accurately)

ddouble v1 = 0.5;
double n1 = (double)v1;

decimal (approximately)

ddouble v1 = 0.1m;
decimal n1 = (decimal)v1;

string (approximately)

ddouble v2 = "3.14e0";
string s0 = v2.ToString();
string s1 = v2.ToString("E8");
string s2 = $"{v2:E8}";

I/O

BinaryWriter, BinaryReader

Licence

MIT

Author

T.Yoshimura

Product	Compatible and additional computed target framework versions.
.NET	net8.0 is compatible. net8.0-android was computed. net8.0-browser was computed. net8.0-ios was computed. net8.0-maccatalyst was computed. net8.0-macos was computed. net8.0-tvos was computed. net8.0-windows was computed. net9.0 was computed. net9.0-android was computed. net9.0-browser was computed. net9.0-ios was computed. net9.0-maccatalyst was computed. net9.0-macos was computed. net9.0-tvos was computed. net9.0-windows was computed.

Product

.NET

Compatible target framework(s)

Included target framework(s) (in package)

Learn more about Target Frameworks and .NET Standard.

net8.0
- No dependencies.

NuGet packages (12)

Showing the top 5 NuGet packages that depend on TYoshimura.DoubleDouble:

Package	Downloads
TYoshimura.Algebra Linear Algebra	13.2K
TYoshimura.DoubleDouble.Complex Double-Double Complex and Quaternion Implements	6.4K
TYoshimura.CurveFitting Curvefitting - linear, polynomial, pade, arbitrary function	4.5K
TYoshimura.DoubleDouble.Statistic Double-Double Statistic Implements	4.2K
TYoshimura.DoubleDouble.Integrate Double-Double Numerical Integration Implements	3.1K

GitHub repositories

This package is not used by any popular GitHub repositories.

Version	Downloads	Last updated
4.2.6	179	11/22/2024
4.2.5	118	11/22/2024
4.2.4	107	11/21/2024
4.2.3	129	11/18/2024
4.2.2	150	11/17/2024
4.2.1	221	11/14/2024
4.2.0	118	11/13/2024
4.1.0	147	11/13/2024
4.0.3	114	11/8/2024
4.0.2	502	11/7/2024
4.0.1	161	11/1/2024
4.0.0	189	10/31/2024
3.3.4	114	10/23/2024
3.3.3	90	10/21/2024
3.3.2	183	10/14/2024
3.3.1	104	10/13/2024
3.3.0	116	10/13/2024
3.2.9	115	10/11/2024
3.2.8	125	9/18/2024
3.2.7	145	9/10/2024
3.2.6	320	8/22/2024
3.2.5	152	8/22/2024
3.2.4	176	7/12/2024
3.2.3	128	6/9/2024
3.2.2	389	4/26/2024
3.2.1	394	2/22/2024
3.2.0	795	1/20/2024
3.1.6	497	11/12/2023
3.1.5	448	11/3/2023
3.1.4	483	11/3/2023
3.1.3	460	10/30/2023
3.1.2	471	10/28/2023
3.1.1	431	10/28/2023
3.1.0	505	10/21/2023
3.0.9	448	10/20/2023
3.0.8	487	10/19/2023
3.0.7	488	10/14/2023
3.0.6	496	10/13/2023
3.0.5	486	10/12/2023
3.0.4	473	10/11/2023
3.0.3	535	10/8/2023
3.0.2	513	10/7/2023
3.0.1	455	9/30/2023
3.0.0	506	9/30/2023
2.9.8	506	9/29/2023
2.9.7	513	9/16/2023
2.9.6	576	9/9/2023
2.9.5	573	9/9/2023
2.9.4	584	9/8/2023
2.9.3	550	9/8/2023
2.9.2	482	9/6/2023
2.9.1	513	9/5/2023
2.9.0	761	9/4/2023
2.8.6	844	3/18/2023
2.8.5	1,223	3/13/2023
2.8.4	735	3/11/2023
2.8.3	686	2/23/2023
2.8.2	687	2/17/2023
2.8.1	770	2/16/2023
2.8.0	689	2/13/2023
2.7.2	1,805	10/30/2022
2.7.1	812	10/28/2022
2.7.0	839	10/25/2022
2.6.1	834	10/14/2022
2.6.0	876	10/13/2022
2.5.6	877	9/18/2022
2.5.5	883	9/17/2022
2.5.4	828	9/16/2022
2.5.3	844	9/15/2022
2.5.2	826	9/7/2022
2.5.1	884	9/5/2022
2.5.0	2,131	9/4/2022
2.4.5	779	9/3/2022
2.4.4	814	9/2/2022
2.4.3	830	8/31/2022
2.4.2	913	2/8/2022
2.4.1	1,379	1/26/2022
2.4.0	861	1/25/2022
2.3.1	1,008	1/21/2022
2.3.0	972	1/20/2022
2.2.0	872	1/13/2022
2.1.2	910	1/12/2022
2.1.1	891	1/12/2022
2.1.0	673	1/11/2022
2.0.5	813	1/9/2022
2.0.4	747	1/8/2022
2.0.2	704	1/8/2022
2.0.1	726	1/7/2022
2.0.0	732	1/7/2022
1.9.4	722	1/6/2022
1.9.3	702	1/6/2022
1.9.2	766	1/5/2022
1.9.0	702	1/5/2022
1.8.0	694	1/4/2022
1.7.0	704	1/3/2022
1.6.1	713	12/25/2021
1.6.0	1,248	12/25/2021
1.5.2	669	12/22/2021
1.5.1	744	12/22/2021
1.5.0	732	12/22/2021
1.4.3	872	12/11/2021
1.4.2	840	12/11/2021
1.4.1	731	12/2/2021
1.4.0	1,215	12/1/2021

fix: bernoulli thread safe