Skip to content

Navigation Menu

Sign in
Appearance settings

Search code, repositories, users, issues, pull requests...

Provide feedback

We read every piece of feedback, and take your input very seriously.

Saved searches

Use saved searches to filter your results more quickly
Sign up
Appearance settings

tk-yoshimura/MultiPrecision

Repository files navigation

MultiPrecision

MultiPrecision Arithmetic Implements

Requirement

.NET 10.0

AVX2 suppoted CPU. (Intel:Haswell(2013)-, AMD:Excavator(2015)-)

Install

Download DLL
Download Nuget

More Functions ?

DoubleDouble (31-32 digits)

Spec

Exponent : ±2147483647
Mantissa : 128-32768 bits
Round: half away from zero
MaxValue: ±8.808065x10^646456992

Types

type mantissa bits significant digits note
MultiPrecision<Pow2.N4> 128 34 Fastest
MultiPrecision<Pow2.N8> 256 73 Fast
MultiPrecision<Pow2.N16> 512 150 Standard
MultiPrecision<Pow2.N32> 1024 304
MultiPrecision<Pow2.N64> 2048 612 Slow
MultiPrecision<Pow2.N128> 4096 1229
MultiPrecision<Pow2.N256> 8192 2462 Very slow
MultiPrecision<Pow2.N512> 16384 4928
MultiPrecision<Pow2.N1024> 32768 9860 Not recommended
MultiPrecision<N> Length x 32 Length x 9.6 - 4 public struct N : IConstant {
public int Value => Length;
}

Functions

function domain mantissa error bits note
MultiPrecision<N>.Sqrt(x) [0,+inf) 1
MultiPrecision<N>.Cbrt(x) (-inf,+inf) 1
MultiPrecision<N>.Log2(x) (0,+inf) 0
MultiPrecision<N>.Log(x) (0,+inf) 1
MultiPrecision<N>.Log10(x) (0,+inf) 1
MultiPrecision<N>.Log1p(x) (-1,+inf) 1 log(1+x)
MultiPrecision<N>.Pow2(x) (-inf,+inf) 0
MultiPrecision<N>.Pow(x, y) (-inf,+inf) 1
MultiPrecision<N>.Pow10(x) (-inf,+inf) 1
MultiPrecision<N>.Exp(x) (-inf,+inf) 1
MultiPrecision<N>.Expm1(x) (-inf,+inf) 1 exp(x)-1
MultiPrecision<N>.Sin(x) (-inf,+inf) 1
MultiPrecision<N>.Cos(x) (-inf,+inf) 1
MultiPrecision<N>.Tan(x) (-inf,+inf) 2
MultiPrecision<N>.SinPi(x) (-inf,+inf) 0 sin(πx)
MultiPrecision<N>.CosPi(x) (-inf,+inf) 0 cos(πx)
MultiPrecision<N>.TanPi(x) (-inf,+inf) 1 tan(πx)
MultiPrecision<N>.Sinh(x) (-inf,+inf) 2
MultiPrecision<N>.Cosh(x) (-inf,+inf) 2
MultiPrecision<N>.Tanh(x) (-inf,+inf) 2
MultiPrecision<N>.Asin(x) [-1,1] 2 Accuracy deteriorates near x=-1,1.
MultiPrecision<N>.Acos(x) [-1,1] 2 Accuracy deteriorates near x=-1,1.
MultiPrecision<N>.Atan(x) (-inf,+inf) 2
MultiPrecision<N>.Atan2(y, x) (-inf,+inf) 2
MultiPrecision<N>.Asinh(x) (-inf,+inf) 2
MultiPrecision<N>.Acosh(x) [1,+inf) 2
MultiPrecision<N>.Atanh(x) (-1,1) 4 Accuracy deteriorates near x=-1,1.
MultiPrecision<N>.Sinc(x, normalized) (-inf,+inf) 2 normalized: x -> πx
MultiPrecision<N>.Sinhc(x) (-inf,+inf) 3
MultiPrecision<N>.Erf(x) (-1,1) 2 Length ≤ 256
MultiPrecision<N>.Erfc(x) (0,2) 2 Length ≤ 256
MultiPrecision<N>.InverseErf(x) (-1,1) 2 Length ≤ 256
MultiPrecision<N>.InverseErfc(x) (0,2) 4 Length ≤ 256
MultiPrecision<N>.LogGamma(x) (0,+inf) 2 Accuracy deteriorates near x=0.
Length ≤ 256
MultiPrecision<N>.Gamma(x) (-inf,+inf) 2 Accuracy deteriorates near non-positive intergers.
Length ≤ 256
MultiPrecision<N>.Digamma(x) (-inf,+inf) 2 Accuracy deteriorates near non-positive intergers and zero points.
Length ≤ 256
MultiPrecision<N>.BesselJ(nu, z) (-inf,+inf) 2 Accuracy deteriorates near zero points.
(error ≤ 2^-(mantissa bits + 64))
Length ≤ 65
abs(nu) ≤ 64
MultiPrecision<N>.BesselY(nu, z) (-inf,+inf) 2 Accuracy deteriorates near zero points.
(error ≤ 2^-(mantissa bits + 64))
Length ≤ 65
abs(nu) ≤ 64
MultiPrecision<N>.BesselI(nu, z) [0,+inf) 2 Length ≤ 65
abs(nu) ≤ 64
MultiPrecision<N>.BesselK(nu, z) [0,+inf) 2 Length ≤ 65
abs(nu) ≤ 64
MultiPrecision<N>.Jinc(x) (-inf,+inf) 3
MultiPrecision<N>.EllipticK(m) [0,1] 1 k: elliptic modulus, m=k^2
MultiPrecision<N>.EllipticE(m) [0,1] 1 k: elliptic modulus, m=k^2
MultiPrecision<N>.EllipticPi(n, m) [0,1] 1 k: elliptic modulus, m=k^2
MultiPrecision<N>.Ldexp(x, y) (-inf,+inf) N/A
MultiPrecision<N>.Random(random) N/A N/A generation uniform random [0, 1)
MultiPrecision<N>.Min(x, y) N/A N/A
MultiPrecision<N>.Max(x, y) N/A N/A
MultiPrecision<N>.Floor(x) N/A N/A
MultiPrecision<N>.Ceiling(x) N/A N/A
MultiPrecision<N>.Round(x) N/A N/A
MultiPrecision<N>.Truncate(x) N/A N/A
IEnumerable<MultiPrecision<N>>.Sum() N/A N/A kahan summation
IEnumerable<MultiPrecision<N>>.Average() N/A N/A kahan summation
IEnumerable<MultiPrecision<N>>.Variance() N/A N/A population variance
IEnumerable<MultiPrecision<N>>.Min() N/A N/A
IEnumerable<MultiPrecision<N>>.Max() N/A N/A

Constants

constant value note
MultiPrecision<N>.Pi 3.141592653589793238462... Pi
MultiPrecision<N>.E 2.718281828459045235360... Napier's E
MultiPrecision<N>.Sqrt2 1.414213562373095048801... Sqrt(2)
MultiPrecision<N>.Lg2 0.301029995663981195213... log10(2)
lg:=log10 (ISO 80000-2-12.6)
MultiPrecision<N>.Lb10 3.321928094887362347870... log2(10)
lb:=log2 (ISO 80000-2-12.7)
MultiPrecision<N>.Ln2 0.693147180559945309417... log(2)
ln:=log (ISO 80000-2-12.5)
MultiPrecision<N>.LbE 1.442695040888963407359... log2(e)
MultiPrecision<N>.EulerGamma 0.577215664901532860606... Euler's Gamma
MultiPrecision<N>.Zeta3 1.202056903159594285399... ζ(3), Apery const.
MultiPrecision<N>.Zeta5 1.036927755143369926331... ζ(5)
MultiPrecision<N>.Zeta7 1.008349277381922826839... ζ(7)

Sequence

sequence note
MultiPrecision<N>.TaylorSequence Taylor, 1/n!
MultiPrecision<N>.BernoulliSequence Bernoulli, B(2k)
MultiPrecision<N>.StirlingSequence Stirling, Gamma convergent series, Bayes(1763)
MultiPrecision<N>.HarmonicNumber HarmonicNumber, H_n

Coefficient

coefficient note
MultiPrecision<N>.ChebyshevCoef Chebyshev, C(n, m)

Casts

  • long (accurately)
MultiPrecision<N> v0 = 123;
long n0 = (long)v0;
  • double (accurately)
MultiPrecision<N> v1 = 0.5;
double n1 = (double)v1;
  • decimal (approximately)
MultiPrecision<N> v1 = 0.1m;
decimal n1 = (decimal)v1;
  • string (approximately)
MultiPrecision<N> 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

AltStyle によって変換されたページ (->オリジナル) /