1:  using Luschny.Math.Arithmetic;

   2:   

   3:  namespace Luschny.Math.Factorial

   4:  {

   5:      public class FactorialDifference : IFactorialFunction

   6:      {

   7:          public FactorialDifference() { }

   8:   

   9:          public string Name

  10:          {

  11:              get { return "Difference"; }

  12:          }

  13:   

  14:          public Xint Factorial(int n)

  15:          {

  16:              if (n < 0)

  17:              {

  18:                  throw new System.ArgumentOutOfRangeException("n",

  19:                        Name + ": n >= 0 required, but was " + n);

  20:              }

  21:   

  22:              if (n < 2) return Xint.One;

  23:   

  24:              Xint f;

  25:   

  26:              switch (n % 4)

  27:              {

  28:                  case 1: f = (Xint) n; break;

  29:                  case 2: f = (Xint)((long)n * (n - 1)); break;

  30:                  case 3: f = (Xint)((long)n * (n - 1) * (n - 2)); break;

  31:                  default: f = Xint.One; break;

  32:              }

  33:   

  34:              long prod = 24;

  35:              long diff1 = 1656;

  36:              long diff2 = 8544;

  37:              long diff3 = 13056;

  38:   

  39:              int i = n / 4;

  40:              while (i-- > 0)

  41:              {

  42:                  f = f * prod; 

  43:                  prod += diff1;

  44:                  diff1 += diff2;

  45:                  diff2 += diff3;

  46:                  diff3 += 6144;

  47:              }

  48:              return f;

  49:          }

  50:      }

  51:  }  // endOfFactorialDifference