Monday, November 30, 2015

Advent Programming Contest 2015

An Advent calendar is a special calendar used to count or celebrate the days in anticipation of Christmas. Advent calendars typically begin on December 1 and provide a window to open until December 24. Usually they have windows, which you can open each day containing some chocolate or other stuff. But what is better to kill some time until Christmas, Hanukkah, Yule, Kwanzaa, Diwali, Boxing Day, etc. than an Advent calendar giving you a programming problem every day?

The Advent Programming Contest, being organized by the IEEE Student Branch Klagenfurt will provide a new problem every day from December 1st to December 24th. You can submit solutions any day until the contest ends on December 26. You can choose to use C, C++, C#, Java, Perl, Python 2.x or Python 3.x as programming language. The programming tasks can be solved with short programs (typically less than 100 lines of code). Until a solution is correct you can submit your program as often as you want (but please don't spam our server). The number of tries will not be a criterion for determining your score. The idea is to do it just for fun, but we will try to announce a winner after the contest is closed. The event is open to everyone. There are separate categories for pupils, university students and others. If you want to participate, please register at (Registration is also possible after 1st December)

Tuesday, November 24, 2015

Random Numbers in Java: Comparison of java.util.random, Xorshift, and PCG

In a previous post, we have shown how to replace the Java random number generator with a faster Xorshift algorithm, which also has nicer properties than the Java random number generator which was implemented in 1995.

Melissa E. O’Neill from Harvey Mudd College suggests a new class of random number generators called PCG. For a detailed description, see her paper "PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation".

Like the Xorshift algorithm, PCG is using a couple of shift and bitwise logical operators to generate random integers. Typically this is faster that Java's linear congruential generator. We have implemented a simple version of the PCG algorithm in order to compare its performance to java.util.random and our Xorshift implementation.

The best way to replace the Java random generator in our opinion is to make a subclass of java.util.random and to overwrite the next() method. For Xorshift, the algorithm is as follows:

import java.util.Random;

 * A subclass of java.util.random that implements the 
 * Xorshift random number generator

public class XSRandom extends Random {
 private long seed;

 public XSRandom(long seed) {
  this.seed = seed;

 protected int next(int nbits) {
  long x = seed;
  x ^= (x << 21);
  x ^= (x >>> 35);
  x ^= (x << 4);
  seed = x;
  x &= ((1L << nbits) - 1);
  return (int) x;

We implemented the PCG algorithm in Java based on the minimal C code example by M.E. O'Neill at

import java.util.Random;

 * A subclass of java.util.random that implements the 
 * PCG32 random number generator
 * Based on the minimal code example by M.E. O'Neill /
 * Licensed under Apache License 2.0

public class PCGRandom extends Random {
 private long inc;
 private long state;
 public PCGRandom(long seed) {
  this.state = seed;

 public PCGRandom(long seed, long initseq) {
  // initseq selects the output sequence for the RNG
  this.state = seed;;

 protected int next(int nbits) {
  long oldstate=state;
  // Advance internal state
  state=oldstate * 6364136223846793005L + (inc | 1);
  // Calculate output function (XSH RR), uses old state for max ILP
  long xorshifted = ((oldstate >> 18) ^ oldstate) >> 27;
  long rot = oldstate >> 59;
  return (int) ((xorshifted >> rot) | (xorshifted << ((-rot) & 31)));

To use the class in legacy code, you may also instantiate an XSRandom object and assign it to a java.util.Random variable:
  java.util.Random rand = new XSRandom(); // or new PCGRandom
All method calls to rand are then using the new implementation.

The PCG algorithm comes with better properties regarding its period. But what about the performance?
We tested the performance by calculating 107 random numbers subsequently, repeating this 10 times with different starting seeds. Then we compared the average execution time for a program compiled under Java 8 running single threaded on an core i7 notebook computer. Results show that for our implementation, the PCG algorithm has a very similar execution time to the original Java random generator, while the Xorshift is significantly faster.

Execution time of java.util.random, Xorshift, and PCG. Please note that y axis starts at 10 ns.
So if you mainly care about speed, go for Xorshift. If statistical quality is important, go for PCG. If you want a bad random number generator and have a lot of time, stick with java.util.random.