TYoshimura.DoubleDouble 3.1.0

.NET 7.0 This package targets .NET 7.0. The package is compatible with this framework or higher.
There is a newer version of this package available.
See the version list below for details. 
dotnet add package TYoshimura.DoubleDouble --version 3.1.0                

                    
                

            
NuGet\Install-Package TYoshimura.DoubleDouble -Version 3.1.0
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="3.1.0" />
For projects that support PackageReference, copy this XML node into the project file to reference the package. 
paket add TYoshimura.DoubleDouble --version 3.1.0                

                    
                

            
#r "nuget: TYoshimura.DoubleDouble, 3.1.0"
#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=3.1.0

// Install TYoshimura.DoubleDouble as a Cake Tool
#tool nuget:?package=TYoshimura.DoubleDouble&version=3.1.0

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
stat 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.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. 
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
TYoshimura.DoubleDouble.Complex

Double-Double Complex and Quaternion Implements
TYoshimura.CurveFitting

Curvefitting - linear, polynomial, pade, arbitrary function
TYoshimura.DoubleDouble.Statistic

Double-Double Statistic Implements
TYoshimura.DoubleDouble.Integrate

Double-Double Numerical Integration Implements

GitHub repositories

This package is not used by any popular GitHub repositories.

Version Downloads Last updated
4.2.1 7 11/14/2024
4.2.0 33 11/13/2024
4.1.0 77 11/13/2024
4.0.3 69 11/8/2024
4.0.2 78 11/7/2024
4.0.1 106 11/1/2024
4.0.0 147 10/31/2024
3.3.4 84 10/23/2024
3.3.3 59 10/21/2024
3.3.2 156 10/14/2024
3.3.1 75 10/13/2024
3.3.0 73 10/13/2024
3.2.9 88 10/11/2024
3.2.8 99 9/18/2024
3.2.7 120 9/10/2024
3.2.6 286 8/22/2024
3.2.5 129 8/22/2024
3.2.4 153 7/12/2024
3.2.3 103 6/9/2024
3.2.2 370 4/26/2024
3.2.1 372 2/22/2024
3.2.0 742 1/20/2024
3.1.6 472 11/12/2023
3.1.5 438 11/3/2023
3.1.4 473 11/3/2023
3.1.3 450 10/30/2023
3.1.2 463 10/28/2023
3.1.1 422 10/28/2023
3.1.0 497 10/21/2023
3.0.9 437 10/20/2023
3.0.8 478 10/19/2023
3.0.7 479 10/14/2023
3.0.6 487 10/13/2023
3.0.5 478 10/12/2023
3.0.4 462 10/11/2023
3.0.3 525 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
2.9.6 567 9/9/2023
2.9.5 563 9/9/2023
2.9.4 575 9/8/2023
2.9.3 540 9/8/2023
2.9.2 473 9/6/2023
2.9.1 502 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
2.8.3 669 2/23/2023
2.8.2 669 2/17/2023
2.8.1 753 2/16/2023
2.8.0 666 2/13/2023
2.7.2 1,764 10/30/2022
2.7.1 790 10/28/2022
2.7.0 805 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 2,096 9/4/2022
2.4.5 755 9/3/2022
2.4.4 790 9/2/2022
2.4.3 789 8/31/2022
2.4.2 882 2/8/2022
2.4.1 1,349 1/26/2022
2.4.0 831 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
2.0.1 696 1/7/2022
2.0.0 701 1/7/2022
1.9.4 691 1/6/2022
1.9.3 669 1/6/2022
1.9.2 718 1/5/2022
1.9.0 672 1/5/2022
1.8.0 664 1/4/2022
1.7.0 667 1/3/2022
1.6.1 681 12/25/2021
1.6.0 1,210 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
1.4.1 697 12/2/2021
1.4.0 1,183 12/1/2021

add rcpgamma, fix invgamma(near singular point)