TYoshimura.DoubleDouble 3.2.1

dotnet add package TYoshimura.DoubleDouble --version 3.2.1
NuGet\Install-Package TYoshimura.DoubleDouble -Version 3.2.1
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="3.2.1" />
For projects that support PackageReference, copy this XML node into the project file to reference the package.
paket add TYoshimura.DoubleDouble --version 3.2.1
#r "nuget: TYoshimura.DoubleDouble, 3.2.1"
#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=3.2.1

// Install TYoshimura.DoubleDouble as a Cake Tool
#tool nuget:?package=TYoshimura.DoubleDouble&version=3.2.1

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 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.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 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.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.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 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. 
Compatible target framework(s)
Included target framework(s) (in package)
Learn more about Target Frameworks and .NET Standard.
  • net8.0

    • No dependencies.

NuGet packages (8)

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

Package Downloads
TYoshimura.Algebra

Linear Algebra

TYoshimura.CurveFitting

Curvefitting - linear, polynomial, pade, arbitrary function

TYoshimura.DoubleDouble.Complex

Double-Double Complex and Quaternion Implements

TYoshimura.DoubleDouble.Integrate

Double-Double Numerical Integration Implements

TYoshimura.DoubleDouble.Differentiate

Double-Double Numerical Differentiation Implements

GitHub repositories

This package is not used by any popular GitHub repositories.

Version Downloads Last updated
3.2.1 235 2/22/2024
3.2.0 433 1/20/2024
3.1.6 431 11/12/2023
3.1.5 402 11/3/2023
3.1.4 438 11/3/2023
3.1.3 415 10/30/2023
3.1.2 429 10/28/2023
3.1.1 395 10/28/2023
3.1.0 464 10/21/2023
3.0.9 406 10/20/2023
3.0.8 444 10/19/2023
3.0.7 436 10/14/2023
3.0.6 452 10/13/2023
3.0.5 450 10/12/2023
3.0.4 432 10/11/2023
3.0.3 482 10/8/2023
3.0.2 477 10/7/2023
3.0.1 412 9/30/2023
3.0.0 463 9/30/2023
2.9.8 461 9/29/2023
2.9.7 463 9/16/2023
2.9.6 519 9/9/2023
2.9.5 521 9/9/2023
2.9.4 540 9/8/2023
2.9.3 514 9/8/2023
2.9.2 440 9/6/2023
2.9.1 474 9/5/2023
2.9.0 679 9/4/2023
2.8.6 774 3/18/2023
2.8.5 1,118 3/13/2023
2.8.4 691 3/11/2023
2.8.3 642 2/23/2023
2.8.2 623 2/17/2023
2.8.1 724 2/16/2023
2.8.0 638 2/13/2023
2.7.2 1,711 10/30/2022
2.7.1 759 10/28/2022
2.7.0 769 10/25/2022
2.6.1 776 10/14/2022
2.6.0 824 10/13/2022
2.5.6 823 9/18/2022
2.5.5 823 9/17/2022
2.5.4 774 9/16/2022
2.5.3 793 9/15/2022
2.5.2 777 9/7/2022
2.5.1 837 9/5/2022
2.5.0 2,004 9/4/2022
2.4.5 727 9/3/2022
2.4.4 764 9/2/2022
2.4.3 761 8/31/2022
2.4.2 851 2/8/2022
2.4.1 1,298 1/26/2022
2.4.0 809 1/25/2022
2.3.1 940 1/21/2022
2.3.0 911 1/20/2022
2.2.0 808 1/13/2022
2.1.2 850 1/12/2022
2.1.1 833 1/12/2022
2.1.0 622 1/11/2022
2.0.5 750 1/9/2022
2.0.4 680 1/8/2022
2.0.2 648 1/8/2022
2.0.1 669 1/7/2022
2.0.0 678 1/7/2022
1.9.4 659 1/6/2022
1.9.3 643 1/6/2022
1.9.2 688 1/5/2022
1.9.0 647 1/5/2022
1.8.0 628 1/4/2022
1.7.0 637 1/3/2022
1.6.1 658 12/25/2021
1.6.0 1,151 12/25/2021
1.5.2 613 12/22/2021
1.5.1 688 12/22/2021
1.5.0 674 12/22/2021
1.4.3 814 12/11/2021
1.4.2 785 12/11/2021
1.4.1 668 12/2/2021
1.4.0 1,152 12/1/2021

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