Boost random number generator

Question

This code is adapted from the boost manual at http://www.boost.org/doc/libs/1_42_0/libs/random/index.html:

#include <iostream>
#include "boost/random.hpp"
#include "boost/generator_iterator.hpp"
using namespace std;

int main() {
      typedef boost::mt19937 RNGType;
      RNGType rng;
      boost::uniform_int<> one_to_six( 1, 6 );
      boost::variate_generator< RNGType, boost::uniform_int<> >
                    dice(rng, one_to_six);
      for ( int i = 0; i < 6; i++ ) {
          int n  = dice();
          cout << n << endl;
     }
}

To explain the bits:

• mt19937 is the mersenne twister generator,which generates the raw random numbers. A typedef is used here so you can easily change random number generator type.

• rng is an instance of the twister generator.

• one_to_six is an instance of a distribution. This specifies the numbers we want to generate and the distribution they follow. Here we want 1 to 6, distributed evenly.

• dice is the thing that takes the raw numbers and the distribution, and creates for us the numbers we actually want.

• dice() is a call to operator() for the dice object, which gets the next random number following the distribution, simulating a random six-sided dice throw.

As it stands, this code produces the same sequence of dice throws each time. You can randomise the generator in its constructor:

 RNGType rng( time(0) );   

or by using its seed() member.

I found this link which gives a good overview of properties of different random number generators. I have copied the table from above link for convenience:

+-----------------------+-------------------+-----------------------------+------------------------+
|       generator       | length of cycle   | approx. memory requirements | approx. relative speed |
+-----------------------+-------------------+-----------------------------+------------------------+
| minstd_rand           | 2^31-2            | sizeof(int32_t)             |                     40 |
| rand48                | 2^48-1            | sizeof(uint64_t)            |                     80 |
| lrand48 (C library)   | 2^48-1            | -                           |                     20 |
| ecuyer1988            | approx. 2^61      | 2*sizeof(int32_t)           |                     20 |
| kreutzer1986          | ?                 | 1368*sizeof(uint32_t)       |                     60 |
| hellekalek1995        | 2^31-1            | sizeof(int32_t)             |                      3 |
| mt11213b              | 2^11213-1         | 352*sizeof(uint32_t)        |                    100 |
| mt19937               | 2^19937-1         | 625*sizeof(uint32_t)        |                    100 |
| lagged_fibonacci607   | approx. 2^32000   | 607*sizeof(double)          |                    150 |
| lagged_fibonacci1279  | approx. 2^67000   | 1279*sizeof(double)         |                    150 |
| lagged_fibonacci2281  | approx. 2^120000  | 2281*sizeof(double)         |                    150 |
| lagged_fibonacci3217  | approx. 2^170000  | 3217*sizeof(double)         |                    150 |
| lagged_fibonacci4423  | approx. 2^230000  | 4423*sizeof(double)         |                    150 |
| lagged_fibonacci9689  | approx. 2^510000  | 9689*sizeof(double)         |                    150 |
| lagged_fibonacci19937 | approx. 2^1050000 | 19937*sizeof(double)        |                    150 |
| lagged_fibonacci23209 | approx. 2^1200000 | 23209*sizeof(double)        |                    140 |
| lagged_fibonacci44497 | approx. 2^2300000 | 44497*sizeof(double)        |                     60 |
+-----------------------+-------------------+-----------------------------+------------------------+

length of cycle: length of random number sequence before it starts repeating

There's no one-size-fits-all RNG. Sometimes statistical properties are important, sometimes cryptology, sometimes raw speed.