MultiPrecision

MultiPrecision Arithmetic Implements

Requirement

.NET 8.0

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