Fast Factorial Functions

There are five algorithms which everyone who wants to compute the factorial n! = 1.2.3...n 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.
• If you do not attach great importance to high performance then get a BigInteger library and use:

  BigInt recfact(long start, long n) {
      long i;
      if (n <= 16) { 
          BigInt r = new BigInt(start);
          for (i = start + 1; i < start + n; i++) r *= i;
          return r;
      }
      i = n / 2;
      return recfact(start, i) * recfact(start + i, n - i);
  }
  BigInt factorial(long n) { return recfact(1, n); }
  

• 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);} Just don't use it!