TYoshimura.DoubleDouble 2.8.6

.NET 6.0 
dotnet add package TYoshimura.DoubleDouble --version 2.8.6
NuGet\Install-Package TYoshimura.DoubleDouble -Version 2.8.6
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="2.8.6" />
For projects that support PackageReference, copy this XML node into the project file to reference the package. 
paket add TYoshimura.DoubleDouble --version 2.8.6
#r "nuget: TYoshimura.DoubleDouble, 2.8.6"
#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. 
// Install TYoshimura.DoubleDouble as a Cake Addin
#addin nuget:?package=TYoshimura.DoubleDouble&version=2.8.6

// Install TYoshimura.DoubleDouble as a Cake Tool
#tool nuget:?package=TYoshimura.DoubleDouble&version=2.8.6

DoubleDouble

Double-Double Arithmetic and Special Function Implements

Requirement

.NET 6.0

Install

Download DLL
Download Nuget

More Precision ?

MultiPrecision

Type

type mantissa bits significant digits
ddouble 104 30

Epsilon: 2^-968 = 4.00833e-292
MaxValue : 2^1024 = 1.79769e308

Functions

function domain mantissa error bits note usage
sqrt [0,+inf) 2 ddouble.Sqrt(x)
cbrt (-inf,+inf) 2 ddouble.Cbrt(x)
log2 (0,+inf) 2 ddouble.Log2(x)
log (0,+inf) 3 ddouble.Log(x)
log10 (0,+inf) 3 ddouble.Log10(x)
log1p (-1,+inf) 3 log(1+x) ddouble.Log1p(x)
pow2 (-inf,+inf) 1 ddouble.Pow2(x)
pow (-inf,+inf) 2 ddouble.Pow(x, y)
pow10 (-inf,+inf) 2 ddouble.Pow10(x)
exp (-inf,+inf) 2 ddouble.Exp(x)
expm1 (-inf,+inf) 2 exp(x)-1 ddouble.Expm1(x)
sin (-inf,+inf) 2 ddouble.Sin(x)
cos (-inf,+inf) 2 ddouble.Cos(x)
tan (-inf,+inf) 3 ddouble.Tan(x)
sinpi (-inf,+inf) 1 sin(πx) ddouble.SinPI(x)
cospi (-inf,+inf) 1 cos(πx) ddouble.CosPI(x)
tanpi (-inf,+inf) 2 tan(πx) ddouble.TanPI(x)
sinh (-inf,+inf) 2 ddouble.Sinh(x)
cosh (-inf,+inf) 2 ddouble.Cosh(x)
tanh (-inf,+inf) 2 ddouble.Tanh(x)
asin [-1,1] 2 Accuracy deteriorates near x=-1,1. ddouble.Asin(x)
acos [-1,1] 2 Accuracy deteriorates near x=-1,1. ddouble.Acos(x)
atan (-inf,+inf) 2 ddouble.Atan(x)
atan2 (-inf,+inf) 2 ddouble.Atan2(y, x)
arsinh (-inf,+inf) 2 ddouble.Arsinh(x)
arcosh [1,+inf) 2 ddouble.Arcosh(x)
artanh (-1,1) 4 Accuracy deteriorates near x=-1,1. ddouble.Artanh(x)
sinc (-inf,+inf) 2 ddouble.Sinc(x, normalized)
sinhc (-inf,+inf) 3 ddouble.Sinhc(x)
gamma (-inf,+inf) 2 Accuracy deteriorates near non-positive intergers. If x is Natual number lass than 35, an exact integer value is returned. ddouble.Gamma(x)
loggamma (0,+inf) 4 ddouble.LogGamma(x)
digamma (-inf,+inf) 4 Near the positive root, polynomial interpolation is used. ddouble.Digamma(x)
polygamma (-inf,+inf) 4 Accuracy deteriorates near non-positive intergers. n ≤ 16 ddouble.Polygamma(n, x)
inverse_gamma [1,+inf) 4 gamma^-1(x) ddouble.InverseGamma(x)
lower_incomplete_gamma [0,+inf) 4 nu ≤ 128 ddouble.LowerIncompleteGamma(nu, x)
upper_incomplete_gamma [0,+inf) 4 nu ≤ 128 ddouble.UpperIncompleteGamma(nu, x)
beta [0,+inf) 4 ddouble.Beta(a, b)
incomplete_beta [0,1] 4 Accuracy decreases when the radio of a,b is too large. a,b ≤ 64 ddouble.IncompleteBeta(x, a, b)
erf (-inf,+inf) 3 ddouble.Erf(x)
erfc (-inf,+inf) 3 ddouble.Erfc(x)
inverse_erf (-1,1) 3 ddouble.InverseErf(x)
inverse_erfc (0,2) 3 ddouble.InverseErfc(x)
erfi (-inf,+inf) 4 ddouble.Erfi(x)
dawson_f (-inf,+inf) 4 ddouble.DawsonF(x)
bessel_j [0,+inf) 8 Accuracy deteriorates near root. abs(nu) ≤ 16 ddouble.BesselJ(nu, x)
bessel_y [0,+inf) 8 Accuracy deteriorates near the root and at non-interger nu very close (< 2^-25) to the integer. abs(nu) ≤ 16 ddouble.BesselY(nu, x)
bessel_i [0,+inf) 6 Accuracy deteriorates near root. abs(nu) ≤ 16 ddouble.BesselI(nu, x)
bessel_k [0,+inf) 6 Accuracy deteriorates with non-interger nu very close (< 2^-25) to an integer. abs(nu) ≤ 16 ddouble.BesselK(nu, x)
struve_h (-inf,+inf) 4 0 ≤ n ≤ 8 ddouble.StruveH(n, x)
struve_k [0,+inf) 4 0 ≤ n ≤ 8 ddouble.StruveK(n, x)
struve_l (-inf,+inf) 4 0 ≤ n ≤ 8 ddouble.StruveL(n, x)
struve_m [0,+inf) 4 0 ≤ n ≤ 8 ddouble.StruveM(n, x)
elliptic_k [0,1] 4 k: elliptic modulus, m=k^2 ddouble.EllipticK(m)
elliptic_e [0,1] 4 k: elliptic modulus, m=k^2 ddouble.EllipticE(m)
elliptic_pi [0,1] 4 k: elliptic modulus, m=k^2 ddouble.EllipticPi(n, m)
incomplete_elliptic_k [0,2pi] 4 k: elliptic modulus, m=k^2 ddouble.EllipticK(x, m)
incomplete_elliptic_e [0,2pi] 4 k: elliptic modulus, m=k^2 ddouble.EllipticE(x, m)
incomplete_elliptic_pi [0,2pi] 4 k: elliptic modulus, m=k^2 Argument order follows wolfram. ddouble.EllipticPi(n, x, m)
elliptic_theta (-inf,+inf) 4 a=1...4, q ≤ 0.995 ddouble.EllipticTheta(a, x, q)
kepler_e (-inf,+inf) 6 inverse kepler's equation, e(eccentricity) ≤ 128 ddouble.KeplerE(m, e, centered)
agm [0,+inf) 2 ddouble.Agm(a, b)
fresnel_c (-inf,+inf) 4 ddouble.FresnelC(x)
fresnel_s (-inf,+inf) 4 ddouble.FresnelS(x)
ei (-inf,+inf) 4 exponential integral ddouble.Ei(x)
ein (-inf,+inf) 4 complementary exponential integral ddouble.Ein(x)
li [0,+inf) 5 logarithmic integral li(x)=ei(log(x)) ddouble.Li(x)
si (-inf,+inf) 4 sin integral, limit_zero=true: si(x) ddouble.Si(x, limit_zero)
ci [0,+inf) 4 cos integral ddouble.Ci(x)
shi (-inf,+inf) 5 hyperbolic sin integral ddouble.Shi(x)
chi [0,+inf) 5 hyperbolic cos integral ddouble.Chi(x)
lambert_w [-1/e,+inf) 4 ddouble.LambertW(x)
airy_ai (-inf,+inf) 5 Accuracy deteriorates near root. ddouble.AiryAi(x)
airy_bi (-inf,+inf) 5 Accuracy deteriorates near root. ddouble.AiryBi(x)
jacobi_sn (-inf,+inf) 4 k: elliptic modulus, m=k^2 ddouble.JacobiSn(x, m)
jacobi_cn (-inf,+inf) 4 k: elliptic modulus, m=k^2 ddouble.JacobiCn(x, m)
jacobi_dn (-inf,+inf) 4 k: elliptic modulus, m=k^2 ddouble.JacobiDn(x, m)
jacobi_amplitude (-inf,+inf) 4 k: elliptic modulus, m=k^2 ddouble.JacobiAm(x, m)
inverse_jacobi_sn [-1,+1] 4 k: elliptic modulus, m=k^2 ddouble.JacobiArcSn(x, m)
inverse_jacobi_cn [-1,+1] 4 k: elliptic modulus, m=k^2 ddouble.JacobiArcCn(x, m)
inverse_jacobi_dn [0,1] 4 k: elliptic modulus, m=k^2 ddouble.JacobiArcDn(x, m)
carlson_rd [0,+inf) 4 ddouble.CarlsonRD(x, y, z)
carlson_rc [0,+inf) 4 ddouble.CarlsonRC(x, y)
carlson_rf [0,+inf) 4 ddouble.CarlsonRF(x, y, z)
carlson_rj [0,+inf) 4 ddouble.CarlsonRJ(x, y, z, w)
carlson_rg [0,+inf) 4 ddouble.CarlsonRG(x, y, z)
riemann_zeta (-inf,+inf) 3 ddouble.RiemannZeta(x)
hurwitz_zeta (1,+inf) 3 a ≥ 0 ddouble.HurwitzZeta(x, a)
dirichlet_eta (-inf,+inf) 3 ddouble.DirichletEta(x)
polylog (-inf,1] 3 n ∈ [-4,8] ddouble.Polylog(n, x)
owen's_t (-inf,+inf) 5 ddouble.OwenT(h, a)
bump (-inf,+inf) 4 C-infinity smoothness basis function, bump(x)=1/(exp(1/x-1/(1-x))+1) ddouble.Bump(x)
hermite_h (-inf,+inf) 3 n ≤ 64 ddouble.HermiteH(n, x)
laguerre_l (-inf,+inf) 3 n ≤ 64 ddouble.LaguerreL(n, x)
associated_laguerre_l (-inf,+inf) 3 n ≤ 64 ddouble.LaguerreL(n, alpha, x)
legendre_p (-inf,+inf) 3 n ≤ 64 ddouble.LegendreP(n, x)
associated_legendre_p [-1,1] 3 n ≤ 64 ddouble.LegendreP(n, m, x)
chebyshev_t (-inf,+inf) 3 n ≤ 64 ddouble.ChebyshevT(n, x)
chebyshev_u (-inf,+inf) 3 n ≤ 64 ddouble.ChebyshevU(n, x)
zernike_r [0,1] 3 n ≤ 64 ddouble.ZernikeR(n, m, x)
gegenbauer_c (-inf,+inf) 3 n ≤ 64 ddouble.GegenbauerC(n, alpha, x)
jacobi_p [-1,1] 3 n ≤ 64, alpha,beta > -1 ddouble.JacobiP(n, alpha, beta, x)
bernoulli [0,1] 4 n ≤ 64, centered: x->x-1/2 ddouble.Bernoulli(n, x, centered)
mathieu_eigenvalue_a (-inf,+inf) 4 n ≤ 16 ddouble.MathieuA(n, q)
mathieu_eigenvalue_b (-inf,+inf) 4 n ≤ 16 ddouble.MathieuB(n, q)
mathieu_ce (-inf,+inf) 4 n ≤ 16, Accuracy deteriorates when q is very large. ddouble.MathieuC(n, q, x)
mathieu_se (-inf,+inf) 4 n ≤ 16, Accuracy deteriorates when q is very large. ddouble.MathieuS(n, q, x)
ldexp (-inf,+inf) N/A ddouble.Ldexp(x, y)
binomial N/A 1 n ≤ 1000 ddouble.Binomial(n, k)
min N/A N/A ddouble.Min(x, y)
max N/A N/A ddouble.Max(x, y)
floor N/A N/A ddouble.Floor(x)
ceiling N/A N/A ddouble.Ceiling(x)
round N/A N/A ddouble.Round(x)
truncate N/A N/A ddouble.Truncate(x)
array sum N/A N/A IEnumerable<ddouble>.Sum()
array average N/A N/A IEnumerable<ddouble>.Average()
array min N/A N/A IEnumerable<ddouble>.Min()
array max N/A N/A IEnumerable<ddouble>.Max()

Constants

constant value note usage
Pi 3.141592653589793238462... ddouble.PI
Napier's E 2.718281828459045235360... ddouble.E
Euler's Gamma 0.577215664901532860606... ddouble.EulerGamma
ζ(3) 1.202056903159594285399... Apery const. ddouble.Zeta3
ζ(5) 1.036927755143369926331... ddouble.Zeta5
ζ(7) 1.008349277381922826839... ddouble.Zeta7
ζ(9) 1.002008392826082214418... ddouble.Zeta9
Positive root of digamma 1.461632144968362341263... ddouble.DigammaZero
Erdös Borwein constant 1.606695152415291763783... ddouble.ErdosBorwein
Feigenbaum constant 4.669201609102990671853... ddouble.FeigenbaumDelta
Lemniscate constant 2.622057554292119810465... ddouble.LemniscatePI

Sequence

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

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 Versions
.NET net6.0 net6.0-android net6.0-ios net6.0-maccatalyst net6.0-macos net6.0-tvos net6.0-windows net7.0 net7.0-android net7.0-ios net7.0-maccatalyst net7.0-macos net7.0-tvos net7.0-windows
Compatible target framework(s)
Additional computed target framework(s)
Learn more about Target Frameworks and .NET Standard.

  • net6.0

    • No dependencies.

NuGet packages (6)

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
2.8.6 73 3/18/2023
2.8.5 175 3/13/2023
2.8.4 76 3/11/2023
2.8.3 98 2/23/2023
2.8.2 95 2/17/2023
2.8.1 98 2/16/2023
2.8.0 104 2/13/2023
2.7.2 362 10/30/2022
2.7.1 223 10/28/2022
2.7.0 228 10/25/2022
2.6.1 260 10/14/2022
2.6.0 261 10/13/2022
2.5.6 274 9/18/2022
2.5.5 272 9/17/2022
2.5.4 267 9/16/2022
2.5.3 271 9/15/2022
2.5.2 274 9/7/2022
2.5.1 278 9/5/2022
2.5.0 888 9/4/2022
2.4.5 274 9/3/2022
2.4.4 276 9/2/2022
2.4.3 272 8/31/2022
2.4.2 324 2/8/2022
2.4.1 655 1/26/2022
2.4.0 325 1/25/2022
2.3.1 434 1/21/2022
2.3.0 324 1/20/2022
2.2.0 323 1/13/2022
2.1.2 325 1/12/2022
2.1.1 307 1/12/2022
2.1.0 176 1/11/2022
2.0.5 201 1/9/2022
2.0.4 182 1/8/2022
2.0.2 172 1/8/2022
2.0.1 167 1/7/2022
2.0.0 172 1/7/2022
1.9.4 170 1/6/2022
1.9.3 163 1/6/2022
1.9.2 175 1/5/2022
1.9.0 178 1/5/2022
1.8.0 180 1/4/2022
1.7.0 185 1/3/2022
1.6.1 195 12/25/2021
1.6.0 344 12/25/2021
1.5.2 180 12/22/2021
1.5.1 175 12/22/2021
1.5.0 182 12/22/2021
1.4.3 404 12/11/2021
1.4.2 336 12/11/2021
1.4.1 188 12/2/2021
1.4.0 690 12/1/2021

fix resource buildin