TYoshimura.DoubleDouble 2.9.4

There is a newer version of this package available.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

dotnet add package TYoshimura.DoubleDouble --version 2.9.4

NuGet\Install-Package TYoshimura.DoubleDouble -Version 2.9.4

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="2.9.4" />

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

paket add TYoshimura.DoubleDouble --version 2.9.4

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

#r "nuget: TYoshimura.DoubleDouble, 2.9.4"

#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=2.9.4

// Install TYoshimura.DoubleDouble as a Cake Tool
#tool nuget:?package=TYoshimura.DoubleDouble&version=2.9.4

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

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)
root_n	(-inf,+inf)	3		ddouble.RootN(x, n)
log2	(0,+inf)	2		ddouble.Log2(x)
log	(0,+inf)	3		ddouble.Log(x), ddouble.Log(x, b)
log10	(0,+inf)	3		ddouble.Log10(x)
log1p	(-1,+inf)	3	log(1+x)	ddouble.Log1p(x)
pow2	(-inf,+inf)	1		ddouble.Pow2(x)
pow2m1	(-inf,+inf)	2	pow2(x)-1	ddouble.Pow2m1(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) ≤ 256	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)
hypot	N/A	2		ddouble.Hypot(x, y)
min	N/A	N/A		ddouble.Min(x, y)
max	N/A	N/A		ddouble.Max(x, y)
clamp	N/A	N/A		ddouble.Clamp(v, min, max)
copysign	N/A	N/A		ddouble.CopySign(value, sign)
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	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	12.3K
TYoshimura.DoubleDouble.Complex Double-Double Complex and Quaternion Implements	4.8K
TYoshimura.CurveFitting Curvefitting - linear, polynomial, pade, arbitrary function	4.0K
TYoshimura.DoubleDouble.Statistic Double-Double Statistic Implements	3.5K
TYoshimura.DoubleDouble.Integrate Double-Double Numerical Integration Implements	2.7K

GitHub repositories

This package is not used by any popular GitHub repositories.

Version	Downloads	Last updated
4.1.0	0	11/13/2024
4.0.3	67	11/8/2024
4.0.2	73	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	72	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

perf basic func