Introduction

Math Expansion Kit (MathXK) is a free open-source C# special functions math library based on the C++ Boost Math Toolkit.

Benefits:

• Implements over 90 high-quality functions including: factorials, gammas, betas, error functions, C floating point functions, exponential integrals, bessels, elliptical integrals, polynomials, root-finding routines, and more.
• Passes the standard Boost Math tests and is internally tested against an arbitrary precision library.
• .NET Standard 2.0 library
• Licensed under the Boost Software License v1.0: usable for commercial or non-commercial purposes without having to release your source code.

Project Status

The routines have been tested with Windows/Intel x64; testing is required on other platforms.

The statistical distributions remain to be done.

What's New?

• v0.6.0 targets netstandard 2.0 (instead of netstandard 1.1). ValueTuple is no longer a dependency.

Requirements

Using the library (binaries) requires one of the following:

• .NET Core 2.0+
• .NET Framework 4.7+

Compiling the source code requires:

• Visual Studio 2017.3
• C#7+
• MS-Test V2

The source code uses the new .NET Core csproj format (which is unsupported by earlier versions of Visual Studio) and uses C#7 value tuples.

Getting Started

A. Using the Binaries with NuGet:

The easiest way to get started is to get the MathXK package from NuGet.

In Visual Studio:

Use "Manage NuGet Packages..." to search for MathXK. (Make sure to check the "include prerelease" checkbox). Install the latest version.

In Visual Studio Package Manager Console:

Install-Package MathXK -Version 0.6.0-alpha

On the command line:

dotnet add package MathXK --version 0.6.0-alpha

B. Downloading the source code:

If you prefer to work directly with the project, you can clone it to your local machine:

git clone https://github.com/rromeo/MathXK

Quck Start Documentation

The main namespaces in MathXK are:

1. MathXK - Contains the static class Math2, where all the special functions are located.
2. MathXK.Roots - Contains all the root finding routines.
3. MathXK.Exceptions - Contains all the exception classes.

A simple C# program that demonstrates the use of Math Extensions is shown below:

using System;

using MathXK; // Main namespace. Special functions are in Math2
using MathXK.Roots; // Root-finding namespace. Routines are in RootFinder

namespace MathXKExample
{
    class Program
    {
        static void Main(string[] args)
        {
            // Compute Gamma(0.5)
            var result = Math2.Tgamma(0.5);
            Console.WriteLine($"Gamma(0.5) = {result}");

            // Compute Beta(2, 1)
            result = Math2.Beta(2, 1);
            Console.WriteLine($"Beta(2, 1) = {result}");
            
            // Compute Asin(0.5)
            result = SimpleArcSin(0.5);
            Console.WriteLine($"ArcSin(0.5) = {result}");

            // Wait for input to close the console
            Console.Write("Press any key...");
            Console.ReadKey();
        }
        
        /// <summary>Arc Sin using root-finding</summary>
        static double SimpleArcSin(double radians) 
        {
            // the function and its derivative
            Func<double, (double, double)> f = (double x) => {
                var function = Math.Sin(x) - radians; 
                var derivative = Math.Cos(x);
                return (function, derivative);
            };

            var root = RootFinder.NewtonSafe(f, guess: 0, min: -1, max: 1);
            if ( root == null )
                return double.NaN; // Bad calling parameters
            if ( !root.Success )
                return double.NaN; // Root not found
            return root.SolutionX; // Return the root
        }
    }
}

Error Handling

The default behavior of the library is to return NaN for function errors (similar to most System.Math functions). Only constructors and property setters throw exceptions.

If you wish the library to throw exceptions instead of returning NaN, define THROW in the Conditional Compilation Settings for the MathXK project and the unit test project.

License

The Lift Math source code is licensed under the Boost Software License v1.0.

"The Boost license permits the creation of derivative works for commercial or non-commercial use with no legal requirement to release your source code." Boost

For more information, see:

• License text
• Discussion

About

MathXK is maintained by Rocco Romeo.

To report bugs or request new features create a new issue. Contributions are welcome.

For other inquiries, contact Rocco Romeo: rromeo@live.ca

Acknowledgements

Thanks to the people at Boost Math who maintain the terrific Boost Math library. (Special thanks to John Maddock & Paul Bristow!)