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Fast-Factorial-Functions

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Swing, divide and conquer the factorial!

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Download Latest Version (.zip)

- - binomial.go
  - binomial_test.go
- - doublefactorial.go
  - doublefactorial_test.go
- - primefactorial.go
  - primefactorial_test.go
- - primes.go
  - primes_test.go
- - simplefactorial.go
  - simplefactorial_test.go
- - swingfactorial.go
  - swingfactorial_test.go
- - xmath.go
  - xmath_test.go
- go.mod
- - FactorialBench2015.jar
  - README.TXT
- readme.html
- BasicSwingFactorial.jl
- PrimeSwingFactorialJulia.jl
- binomial.cpp
- binomial.h
- ClassDiagram.png
- double_fac_ui.cpp
- doublefactorial.cpp
- lmp.h
- main.cpp
- makefile
- parallelbinomial.cpp
- paralleldoublefactorial.cpp
- parallelschoenhage.cpp
- parallelswing.cpp
- primeswing.cpp
- primeswing.h
- readme.txt
- schoenhage.cpp
- schoenhage.h
- stopwatch.h
- test.h
- xmath.h
- BasicSwingFactorial.pl
- PrimeSwingFactorialGmpy.py
- PrimeSwingFactorialPy.py
- SageMathPrimeSwingFactorial.ipynb
- - Sharith.csproj
- - app.config
  - Application.xaml
  - Application.xaml.cs
  - BrowserForm.cs
  - BrowserForm.resx
  - LoggedTextBox.cs
  - MainWindow.xaml
  - MainWindow.xaml.cs
  - mpir.dll
  - SilverFactorial.csproj
  - silverfactorial.ico
- SilverFactorial64.sln
.gitignore
LICENSE
README.md

// repository documentation

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Fast Factorial Functions
========================

Project status: maintained and up-to-date.

Here you can find implementations of the most efficient algorithms to compute

* the [factorial](http://en.wikipedia.org/wiki/Factorial) function,
* the [double factorial](http://en.wikipedia.org/wiki/Double_factorial#Double_factorial) function,
* the [binomial](http://en.wikipedia.org/wiki/Binomial) function.

See also this nice [overview](http://functions.wolfram.com/GammaBetaErf/Factorial2/introductions/FactorialBinomials/ShowAll.html).

Short guide:

* If you want to study the different algorithms proposed to compute the factorial function 
the best start is to look into this [directory](https://github.com/PeterLuschny/Fast-Factorial-Functions/tree/master/SilverFactorial64/Sharith/Factorial).

* If you just want to study/use the fastest algorithm the best start probably is to read the 
[SageMath implementation](https://github.com/PeterLuschny/Fast-Factorial-Functions/blob/master/SageMathFactorial/SageMathPrimeSwingFactorial.ipynb)
or the [Python implementation](https://github.com/PeterLuschny/Fast-Factorial-Functions/blob/master/PythonFactorial/SwingFactorialPy_gmpy2.py)
or the [Julia implementation](https://github.com/PeterLuschny/Fast-Factorial-Functions/blob/master/JuliaFactorial/PrimeSwingFactorialJulia.jl)
of the prime swing algorithm.

Implementation languages
------------------------

* Project MpirBasedFunctions : C++
* Project SilverFactorial64 : C#
* Project JavaFactorial : Java
* Project GoFactorial : Go
* Project SageMathFactorial : SageMath
* Project PyFactorial : Python
* Project JFactorial : Julia

The C# and the Java version come with a small benchmark program.
Here a screenshot of the [Java](http://www.luschny.de/math/factorial/JavaFactorialBench.png) version
and a screenshot of the [C#](http://www.luschny.de/math/factorial/FastFactorial64.JPG) version.

Browsing the code
-----------------

To browse the code the following two pages might be more convenient: [primes](http://www.luschny.de/math/primes/PrimeSieveForJavaAndCsharp.html) and [factorials](http://www.luschny.de/math/factorial/index.html).

Porting
-------

If you want to port the algorithms to other languages the C# version is recommended as the point of departure.
The [benchmarks](http://www.luschny.de/math/factorial/Benchmark.html) indicate that it is a good idea to start with the [swing algorithm](http://www.luschny.de/math/factorial/csharp/FactorialSwing.cs.html)
or (more demanding to implement, but at least twice as fast) the [prime swing algorithm](http://www.luschny.de/math/factorial/csharp/FactorialPrimeSwing.cs.html).

A good starting point for the binomial function is [here](http://www.luschny.de/math/factorial/FastBinomialFunction.html).

Dependencies
------------

To build the sources you need for

* the C++ version the [MPIR](http://www.mpir.org) library.

* The C# version uses the [MPIR](http://www.mpir.org) library (an interop is provided).

* The Java version needs Mikko Tommila's [Apfloat](http://www.apfloat.org/apfloat_java)
library. If you want to compile the benchmark program additionally Karsten
Lentzsch's [JGoodies](http://www.jgoodies.com/downloads/libraries.html) is needed.

Contributing
------------

Please notify me of any bugs. Want to contribute new algorithms? Great, please contact me.
If you already ported to some other language (Scala, F#, Rust, Ruby, Lisp) then please send 
me your code so I can incorporate it into this repository.

Contributors
---------------

[Sonia Keys](http://soniacodes.wordpress.com) ported the algorithms to [Go](http://golang.org/).

Michael Saupe contributed a performance optimized python3 version with gmpy2.