/******************************************************************************
 *  Compilation:  javac Gamma.java
 *  Execution:    java Gamma 5.6
 *
 *  Reads in a command line input x and prints Gamma(x) and
 *  log Gamma(x). The Gamma function is defined by
 *
 *        Gamma(x) = integral( t^(x-1) e^(-t), t = 0 .. infinity)
 *
 *  Uses Lanczos approximation formula. See Numerical Recipes 6.1.
 *
 *
 *
 ******************************************************************************/

public class Gamma {

   static double logGamma(double x) {
      double tmp = (x - 0.5) * Math.log(x + 4.5) - (x + 4.5);
      double ser = 1.0 + 76.18009173    / (x + 0)   - 86.50532033    / (x + 1)
                       + 24.01409822    / (x + 2)   -  1.231739516   / (x + 3)
                       +  0.00120858003 / (x + 4)   -  0.00000536382 / (x + 5);
      return tmp + Math.log(ser * Math.sqrt(2 * Math.PI));
   }
   static double gamma(double x) { return Math.exp(logGamma(x)); }

   public static void main(String[] args) {
      double x = Double.parseDouble(args[0]);
      StdOut.println("Gamma(" + x + ") = " + gamma(x));
      StdOut.println("log Gamma(" + x + ") = " + logGamma(x));
   }

}