Sdcb.Arithmetic.Gmp 6.2.1

The ID prefix of this package has been reserved for one of the owners of this package by Prefix Reserved
dotnet add package Sdcb.Arithmetic.Gmp --version 6.2.1
NuGet\Install-Package Sdcb.Arithmetic.Gmp -Version 6.2.1
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="Sdcb.Arithmetic.Gmp" Version="6.2.1" />
For projects that support PackageReference, copy this XML node into the project file to reference the package.
paket add Sdcb.Arithmetic.Gmp --version 6.2.1
#r "nuget: Sdcb.Arithmetic.Gmp, 6.2.1"
#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 Sdcb.Arithmetic.Gmp as a Cake Addin
#addin nuget:?package=Sdcb.Arithmetic.Gmp&version=6.2.1

// Install Sdcb.Arithmetic.Gmp as a Cake Tool
#tool nuget:?package=Sdcb.Arithmetic.Gmp&version=6.2.1


Sdcb.Arithmetic is a modern .NET library that can PInvoke to gmp and mpfr, that enable both high performance and best .NET convenience.

Known classes in Sdcb.Arithmetic:

Class Native name Library
GmpInteger mpz_t Sdcb.Arithmetic.Gmp
GmpFloat mpf_t Sdcb.Arithmetic.Gmp
GmpRational mpq_t Sdcb.Arithmetic.Gmp
GmpRandom gmp_randstate_t Sdcb.Arithmetic.Gmp
MpfrFloat mpfr_t Sdcb.Arithmetic.Mpfr

NuGet Packages


Package Id Version License Notes
Sdcb.Arithmetic.Gmp NuGet MIT .NET binding for libgmp
Sdcb.Arithmetic.Gmp.runtime.win64 NuGet LGPL native lib in windows x64
Sdcb.Arithmetic.Gmp.runtime.win32 NuGet LGPL native lib in windows x86
Sdcb.Arithmetic.Gmp.runtime.linux64 NuGet LGPL native lib in Linux x64


Package Id Version License Notes
Sdcb.Arithmetic.Mpfr NuGet MIT .NET binding for libmpfr
Sdcb.Arithmetic.Mpfr.runtime.win64 NuGet LGPL native lib in windows x64
Sdcb.Arithmetic.Mpfr.runtime.win32 NuGet LGPL native lib in windows x86
Sdcb.Arithmetic.Mpfr.runtime.linux64 NuGet LGPL native lib in linux x64

Question - Why not linux-64 can't run in my linux?

The linux-x64 package is compiled using vcpkg in Ubuntu 22.04, so it may not run in other linux distributions.

If you want to run in other linux distributions, you can compile it yourself, or install it using apt or yum or other package manager.

This is the all native dynamic library name in case you wondering(defined in GmpNativeLoader.cs and MpfrNativeLoader.cs):

OS gmp dynamic lib mpfr dynamic lib
Windows gmp-10.dll mpfr-6.dll
MacOS libgmp.10.dylib libmpfr.6.dylib
Others gmp.10 mpfr.6


Calculate 1,000,000 length of π using Sdcb.Arithmetic.Gmp:

// Install NuGet package: Sdcb.Arithmetic.Gmp
// Install NuGet package: windows)
using Sdcb.Arithmetic.Gmp;


GmpFloat CalcPI(int inputDigits = 1_000_000)
    const double DIGITS_PER_TERM = 14.1816474627254776555; // = log(53360^3) / log(10)
    int DIGITS = (int)Math.Max(inputDigits, Math.Ceiling(DIGITS_PER_TERM));
    uint PREC = (uint)(DIGITS * Math.Log2(10));
    int N = (int)(DIGITS / DIGITS_PER_TERM);
    const int A = 13591409;
    const int B = 545140134;
    const int C = 640320;
    const int D = 426880;
    const int E = 10005;
    const double E3_24 = (double)C * C * C / 24;

    using PQT pqt = ComputePQT(0, N);

    GmpFloat pi = new(precision: PREC);
    // pi = D * sqrt((mpf_class)E) * PQT.Q;
    pi.Assign(GmpFloat.From(D, PREC) * GmpFloat.Sqrt((GmpFloat)E, PREC) * (GmpFloat)pqt.Q);
    // pi /= (A * PQT.Q + PQT.T);
    GmpFloat.DivideInplace(pi, pi, GmpFloat.From(A * pqt.Q + pqt.T, PREC));
    return pi;

    PQT ComputePQT(int n1, int n2)
        int m;

        if (n1 + 1 == n2)
            PQT res = new()
                P = GmpInteger.From(2 * n2 - 1)
            GmpInteger.MultiplyInplace(res.P, res.P, 6 * n2 - 1);
            GmpInteger.MultiplyInplace(res.P, res.P, 6 * n2 - 5);

            GmpInteger q = GmpInteger.From(E3_24);
            GmpInteger.MultiplyInplace(q, q, n2);
            GmpInteger.MultiplyInplace(q, q, n2);
            GmpInteger.MultiplyInplace(q, q, n2);
            res.Q = q;

            GmpInteger t = GmpInteger.From(B);
            GmpInteger.MultiplyInplace(t, t, n2);
            GmpInteger.AddInplace(t, t, A);
            GmpInteger.MultiplyInplace(t, t, res.P);
            // res.T = (A + B * n2) * res.P;            
            if ((n2 & 1) == 1) GmpInteger.NegateInplace(t, t);
            res.T = t;

            return res;
            m = (n1 + n2) / 2;
            PQT res1 = ComputePQT(n1, m);
            using PQT res2 = ComputePQT(m, n2);
            GmpInteger p = res1.P * res2.P;
            GmpInteger q = res1.Q * res2.Q;

            // t = res1.T * res2.Q + res1.P * res2.T
            GmpInteger.MultiplyInplace(res1.T, res1.T, res2.Q);
            GmpInteger.MultiplyInplace(res1.P, res1.P, res2.T);
            GmpInteger.AddInplace(res1.T, res1.T, res1.P);
            return new PQT
                P = p,
                Q = q,
                T = res1.T,

public ref struct PQT
    public GmpInteger P;
    public GmpInteger Q;
    public GmpInteger T;

    public readonly void Dispose()

Technical notes

Why choosing struct in class design instead of raw memory IntPtr design?

  • (1) Struct in class design:

    class GmpInteger
      public readonly Mpz_t Raw;
      public unsafe void DoWork()
          fixed (Mpz_t* ptr = &Raw)
    struct Mpz_t
      public int A, B;
      public IntPtr Limbs;
  • (2) Raw memory IntPtr design:

    class GmpInteger : IDisposable
      public readonly IntPtr Raw;
      public unsafe GmpInteger()
          Raw = Marshal.AllocHGlobal(sizeof(Mpz_t));
      public void DoWork()
      public void Dispose()

    Here is some benchmark I tested for both DoWork senario and initialize-dispose senario:


    • init & dispose combines following actions:
      • allocating struct memory
      • calling mpz_init
      • calling mpz_free
      • free the memory
      • Measure the operations-per-seconds, higher ops is better
    • dowork contains following actions:
      • create a GmpFloat to 1.5 with precision=1000(v = 1, a = 1.5)
      • Calling MultiplyInplace(v *= a) 10*1024*1024 times
      • Measure the duration, lower is better

    Here is the tested results in my laptop:

    case/senario init & dispose dowork
    Struct in class 82,055,792 ops 1237ms
    Raw memory IntPtr 15,543,619 ops 1134ms

    As you can see, raw memory IntPtr design will benifits ~8.33% faster in dowork senario above, but struct in class design will be 5.2x faster in init & dispose senario.

    Finally I choosed the struct in class design, here is some existing Raw memory IntPtr design work if you also wants to check or test:

    Struct in class performance results environment:

    In the future, Raw memory IntPtr design can be pick-up if a handy, good performance memory allocator was found.

Product Compatible and additional computed target framework versions.
.NET net5.0 was computed.  net5.0-windows was computed.  net6.0 is compatible.  net6.0-android was computed.  net6.0-ios was computed.  net6.0-maccatalyst was computed.  net6.0-macos was computed.  net6.0-tvos was computed.  net6.0-windows was computed.  net7.0 was computed.  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. 
.NET Core netcoreapp3.1 is compatible. 
Compatible target framework(s)
Included target framework(s) (in package)
Learn more about Target Frameworks and .NET Standard.
  • .NETCoreApp 3.1

    • No dependencies.
  • net6.0

    • No dependencies.

NuGet packages (1)

Showing the top 1 NuGet packages that depend on Sdcb.Arithmetic.Gmp:

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Sdcb.Arithmetic.Mpfr The ID prefix of this package has been reserved for one of the owners of this package by

A modern MPFR arithmetic library dotnet binding

GitHub repositories (1)

Showing the top 1 popular GitHub repositories that depend on Sdcb.Arithmetic.Gmp:

Repository Stars
A modern .NET library that can PInvoke to gmp and mpfr, that enable both high performance and best .NET convenience.
Version Downloads Last updated
6.2.1 296 6/29/2023