TYoshimura.DoubleDouble 3.1.2

There is a newer version of this package available.
See the version list below for details.

dotnet add package TYoshimura.DoubleDouble --version 3.1.2

NuGet\Install-Package TYoshimura.DoubleDouble -Version 3.1.2

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="3.1.2" />

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

paket add TYoshimura.DoubleDouble --version 3.1.2

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

#r "nuget: TYoshimura.DoubleDouble, 3.1.2"

#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.

// Install TYoshimura.DoubleDouble as a Cake Addin
#addin nuget:?package=TYoshimura.DoubleDouble&version=3.1.2

// Install TYoshimura.DoubleDouble as a Cake Tool
#tool nuget:?package=TYoshimura.DoubleDouble&version=3.1.2

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 7.0

Install

Download DLL
Download Nuget

More Precision ?

MultiPrecision

Type

type	mantissa bits	significant digits
ddouble	104	30

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), 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.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.Arsinh(x)	(-inf,+inf)	2
ddouble.Arcosh(x)	[1,+inf)	2
ddouble.Artanh(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.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)	8	Accuracy deteriorates near root. abs(nu) ≤ 16
ddouble.BesselY(nu, x)	[0,+inf)	8	Accuracy deteriorates near the root and at non-interger nu very close (< 2^-25) to the integer. abs(nu) ≤ 16
ddouble.BesselI(nu, x)	[0,+inf)	6	Accuracy deteriorates near root. abs(nu) ≤ 16
ddouble.BesselK(nu, x)	[0,+inf)	6	Accuracy deteriorates with non-interger nu very close (< 2^-25) to an integer. abs(nu) ≤ 16
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.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)	[0,2pi]	4	k: elliptic modulus, m=k^2
ddouble.EllipticE(x, m)	[0,2pi]	4	k: elliptic modulus, m=k^2, incomplete elliptic integral
ddouble.EllipticPi(n, x, m)	[0,2pi]	4	k: elliptic modulus, m=k^2 Argument order follows wolfram. incomplete elliptic integral
ddouble.EllipticTheta(a, x, q)	(-inf,+inf)	4	a=1...4, q ≤ 0.995, incomplete elliptic integral
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.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.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, w)	[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.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.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.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.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	net7.0 is compatible. net7.0-android was computed. net7.0-ios was computed. net7.0-maccatalyst was computed. net7.0-macos was computed. net7.0-tvos was computed. net7.0-windows was computed. net8.0 was computed. 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.

Product

.NET

Compatible target framework(s)

Included target framework(s) (in package)

Learn more about Target Frameworks and .NET Standard.

net7.0
- No dependencies.

NuGet packages (11)

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

Package	Downloads
TYoshimura.Algebra Linear Algebra	12.1K
TYoshimura.DoubleDouble.Complex Double-Double Complex and Quaternion Implements	4.7K
TYoshimura.CurveFitting Curvefitting - linear, polynomial, pade, arbitrary function	3.9K
TYoshimura.DoubleDouble.Statistic Double-Double Statistic Implements	3.4K
TYoshimura.DoubleDouble.Integrate Double-Double Numerical Integration Implements	2.6K

GitHub repositories

This package is not used by any popular GitHub repositories.

Version	Downloads	Last updated
4.0.1	60	11/1/2024
4.0.0	96	10/31/2024
3.3.4	79	10/23/2024
3.3.3	55	10/21/2024
3.3.2	154	10/14/2024
3.3.1	68	10/13/2024
3.3.0	70	10/13/2024
3.2.9	86	10/11/2024
3.2.8	95	9/18/2024
3.2.7	117	9/10/2024
3.2.6	285	8/22/2024
3.2.5	129	8/22/2024
3.2.4	153	7/12/2024
3.2.3	102	6/9/2024
3.2.2	369	4/26/2024
3.2.1	372	2/22/2024
3.2.0	741	1/20/2024
3.1.6	472	11/12/2023
3.1.5	437	11/3/2023
3.1.4	472	11/3/2023
3.1.3	449	10/30/2023
3.1.2	463	10/28/2023
3.1.1	421	10/28/2023
3.1.0	497	10/21/2023
3.0.9	435	10/20/2023
3.0.8	478	10/19/2023
3.0.7	479	10/14/2023
3.0.6	486	10/13/2023
3.0.5	477	10/12/2023
3.0.4	461	10/11/2023
3.0.3	524	10/8/2023
3.0.2	505	10/7/2023
3.0.1	444	9/30/2023
3.0.0	497	9/30/2023
2.9.8	496	9/29/2023
2.9.7	501	9/16/2023
2.9.6	566	9/9/2023
2.9.5	562	9/9/2023
2.9.4	574	9/8/2023
2.9.3	539	9/8/2023
2.9.2	473	9/6/2023
2.9.1	501	9/5/2023
2.9.0	751	9/4/2023
2.8.6	827	3/18/2023
2.8.5	1,205	3/13/2023
2.8.4	719	3/11/2023
2.8.3	668	2/23/2023
2.8.2	668	2/17/2023
2.8.1	752	2/16/2023
2.8.0	665	2/13/2023
2.7.2	1,763	10/30/2022
2.7.1	789	10/28/2022
2.7.0	804	10/25/2022
2.6.1	811	10/14/2022
2.6.0	852	10/13/2022
2.5.6	852	9/18/2022
2.5.5	859	9/17/2022
2.5.4	804	9/16/2022
2.5.3	820	9/15/2022
2.5.2	802	9/7/2022
2.5.1	859	9/5/2022
2.5.0	2,095	9/4/2022
2.4.5	755	9/3/2022
2.4.4	790	9/2/2022
2.4.3	789	8/31/2022
2.4.2	879	2/8/2022
2.4.1	1,349	1/26/2022
2.4.0	830	1/25/2022
2.3.1	977	1/21/2022
2.3.0	937	1/20/2022
2.2.0	841	1/13/2022
2.1.2	878	1/12/2022
2.1.1	861	1/12/2022
2.1.0	643	1/11/2022
2.0.5	783	1/9/2022
2.0.4	717	1/8/2022
2.0.2	673	1/8/2022
2.0.1	695	1/7/2022
2.0.0	699	1/7/2022
1.9.4	690	1/6/2022
1.9.3	669	1/6/2022
1.9.2	718	1/5/2022
1.9.0	671	1/5/2022
1.8.0	664	1/4/2022
1.7.0	666	1/3/2022
1.6.1	681	12/25/2021
1.6.0	1,208	12/25/2021
1.5.2	639	12/22/2021
1.5.1	713	12/22/2021
1.5.0	702	12/22/2021
1.4.3	842	12/11/2021
1.4.2	809	12/11/2021
1.4.1	695	12/2/2021
1.4.0	1,183	12/1/2021

fix bessel near zero