N !


and

There are five algorithms which everyone who wants to compute the factorial n! = 1.2.3...n exactly should know.

  • The algorithm SplitRecursive, because it is simple and the fastest algorithm which does not use prime factorization.
  • The algorithm PrimeSwing, because it is the (asymptotical) fastest algorithm known to compute n!. The algorithm is based on the notion of the 'Swing Numbers' and computes n! via the prime factorization of these numbers.
  • The ingenious algorithm of Moessner which uses only additions! Though of no practical importance (because it is slow), it has the fascination of an unexpected solution.
  • The Poor Man's algorithm which uses no Big-Integer library and can be easily implemented in any computer language and is even fast up to 10000!.
  • The ParallelPrimeSwing algorithm, which is the PrimeSwing algorithm with improved performance using methods of concurrent programming and thus taking advantage of multiple core processors.
  • And here is an algorithm which nobody needs, for the Simple-Minded only:
    long factorial(long n) { return n <= 1 ? 1 : n * factorial(n-1); }  Do not use it if n > 12.
 Content  Link   
A very short description of 21 algorithms for computing
the factorial function n!.		 Algorithms   
Hot! The factorial function, the binomial function, the
double factorial, the swing numbers and an efficient
prime number sieve implemented in Scala and GO.		 FFF-MiniLib  X
Various algorithms implemented in Java, C# and C++. Browse Code   
New (2010): Various benchmark results.
Embarrassing! Testing with GMP 5.0 and MPIR 1.3.		 Benchmarks   
Which algorithm should we choose? Conclusions   
Download a test application and benchmark yourself. Download   
A unique collection! Approximation formulas. Approximations  X
Bounds for Gamma(x+1)/Gamma(x+1/2) Bounds   
Why is Gamma(n)=(n-1)! and not Gamma(n)=n! ? Factorial/Gamma   
You can define the factorial of -n in a meaningful way.
Hadamard's Gamma and a new factorial function.		 Hadamard  X
Not even Wikipedia knows this!
The early history of the factorial function.		 History   
On the notation n! Notation   
For coders only. Go to the page of the day. Binary Split   
New research! The fast double factorial function. Double Factorial  ‼
Primfakultaet ('The Primorial', in German.) Prime Factorial   
Bibliography on Inequalities for the Gamma function. Bibliography   
Exotic Applications:
Inclusions for the Bernoulli and Euler numbers.		 Bernoulli /
Euler		  X
Fast Binomial Function (Binomial Coefficients). Binomial   
A combinatorial generalization of the factorial. Variations   
On Stieltjes' Continued Fraction for the
Gamma Function.		 Stieltjes' CF  X
The ignorance of some western mathematicians.
A deterministic factorial primality test.		 al-Haytham /
Lagrange		   
Number of decimal digits of 10n! Factorial Digits   
Calculate n! for n up to 9.999.999.999 . Calculator   
The retro-factorial page! RPN-Factorial   
Awesome! Permutation trees, the combinatorics of n!.
Download a pdf-poster with 120 permutation trees!		 Perm's n=4
Perm' trees		   
Beautiful! Plots of the factorial (gamma) function. Gamma
LogGamma		   
Fast-Factorial-Functions: The Homepage of Factorial Algorithms. (C) Peter Luschny, 2000-2010.
All information and all source code in this directory is free under the Creative Commons Attribution-ShareAlike 3.0 Unported License (the same license which Wikipedia uses). This page is listed on the famous "Dictionary of Algorithms and Data Structures" at the National Institute of Standards and Technology's web site (NIST). Apr. 2003 / Apr. 2010 : 200,000 visitors! Thank you! 
Postscript: The best algorithms to compute the factorial function are based on the swinging factorial numbers. More on these numbers can be found on here:
Swinging Factorial  Swinging Primes