C.3. Advanced Usage Guide

C.3.1.1. Choosing A Generator

In this version of Random for Swarm there are a total of 36 different generators implemented. If you are a serious simulationist you need to select which one(s) to use for your model.

Here are some factors to consider:

1. We want a generator to have as good statistical properties as possible. We measure this by subjecting the generators to various tests. I have subjected the implemented generators to two sets of tests, Diehard and ENT. (Look in directory /testR6 of the test package.) (The Generators quality table summarizes the test results. The highlights are:

   1. The LCG and SCG generators are of very poor quality (they fail many of the tests), and should never be used. [They are likely to disappear in the next release.]

   2. The lagged-Fibonacci generators (ACG, SWBi, PSWB) all fail the Diehard `Birthday Spacings Test', and are therefore only conditionally recommended for use.

   3. The other 32-bit generators pass all tests, and I therefore have no reason not to recommend them all for use.

   4. The 31-bit generators all fail certain tests because one bit has a constant value. Beyond that they all seem to be ok.

2. We want a generator to have a long enough period for our purpose, and in general the longer the period the better. (However, note that to generate 2⁶⁴ random numbers from a fast generator like MT19937 would take 2.1 million years on a 486/66, so in practice any generator with a period close to 2⁶⁰ or larger will be acceptable.) The PMMLCG generators, although they are of acceptable quality otherwise, have a period less than 2³¹ which we can exhaust in under 3 hours. So use those only for quick `toy' applications.

3. We want a generator to execute efficiently, the faster the better. The Generators data table indicates the execution times for the generators as implemented.

4. We want a generator to take as little resources (memory) as possible. The Generators data table indicates the size of each generator's state in bits.

5. Other things being equal, we want our generator to have a single full period rather than a number of shorter periods, since we may not know whether a particular starting seed will put us into a long or a short subcycle. This disqualifies SWB, and possibly the new MWC and RWC generators (Marsaglia does not say how many periods these generators have, but only gives the period length.)

C.3.1.2. Strategy For Using Random Generators

There are 3 possible strategies for using random generators:

1. Use one single generator for your whole simulation, and have all `users' of randomness (distributions and other objects) call this single generator in an interleaved fashion. For this purpose, generators such as MT19937, TT800, TT775, TT443 (and possibly PSWB and SWB) seem particularly well suited since they have immense periods. The code in random/random.m shows how to connect several distribution objects to a single random generator. The generator randomGenerator supplied there is of class MT19937.

2. Use a single generator of long period, but divide this long period up into a number of non-overlapping (hence statistically independent) segments, and let each `user' of randomness draw their random numbers from separate segments. Doing this requires that we be able to quickly access these separate segments. The `split' generators C2LCGX and C4LCGX implement such a scheme. You can specify at creation how you want the period of these generators subdivided. (See the source code for details.)

3. Use a separate random generator for each `user' of randomness. In this case, you need to make sure that two or more generators of the same type are not started with the same seed, since in this case their output will be highly correlated. Provide your own seeds, or use RANDOMSEED or NEXTSEED.

The distribution objects, if created with the `createWithDefault: aZone' method, will create for themselves a fresh generator, with each class of distribution using a different class of generator. All the generators in this case are initialized with NEXTSEED (or RANDOMSEED, if you start the program with --varyseed).

C.3.1.3. Generator Quality

These tables shows the results of testing the generator objects statistically:

C.3.1.4. More generator data

And this table gives further data about the generators:

C.3.2.1. Random Library: Default Generators

When distributions are created using the createWithDefaults: aZone method, they create their own generator and initialize it with NEXTSEED (or with RANDOMSEED, if you started the program with the --varyseed switch).

The generators used are as follows:

These generators were chosen on the basis of quality and execution speed.

C.3.2.2. Utility Generator And Distributions

There are 4 default random objects defined in random/random.m. These are:

id <MT19937gen> randomGenerator; id <UniformIntegerDist> uniformIntRand; id <UniformUnsignedDist> uniformUnsRand; id <UniformDoubleDist> uniformDblRand;

These objects may be called from anywhere in your program. Note (a): the generator is initialized with NEXTSEED or RANDOMSEED depending on the use of the --varyseed command line option. Note (b): the distribution objects are created without default statistical parameters.