The library implements several types of random number generators, including some proposed in the literature and some found in widely used software. It provides general implementations of the classical statistical tests for random number generators, as well as several others proposed in the literature, and some original ones. These tests can be applied to the generators predefined in the library, user-defined generators, and streams of random numbers stored in files. Specific tests suites for either sequences of uniform random numbers in [0,1] or bit sequences are also available. Basic tools for plotting vectors of points produced by generators are provided as well.
An initial battery of statistical tests for uniform RNGs was offered by the 1969 first edition of Knuth (1997). In popular testing of RNGs, Donald Knuth's tests were supplanted by George Marsaglia's (1996) DIEHARD tests, and DIEHARD has been the standard for several years. To use Marsaglia's program, the user creates a file of three million random numbers, and the program analyzes these numbers. There are some notable difficulties with DIEHARD. First, it is not user-friendly. Second, it does not offer many tests—about 15. Third, the parameters of the tests are fixed, and it is often advantageous to vary them. Fourth, it is not extensible—new tests cannot be added. Fifth, while these tests might have been stringent 10 years ago, they are not now.
TESTU01 offers four groups of modules for analyzing RNGs:
- Implementing (pre-programmed) RNGs;
- implementing specific statistical tests;
- implementing batteries of statistical tests; and
- Applying tests to entire families of RNGs.
When a specific test is applied to a sample of size n produced by an RNG, the p-value of the test usually will remain ‘reasonable’ as the sample size increases until the sample size hits n0, say. After that, the p-value diverges to 0 or 1 with exponential speed. Module 4 allows the researcher to study the interaction between a specific test and the structure of the point sets produced by a given family of RNGs. This technique can be used to determine how large the sample size should be, as a function of the generator's period length, before the generator starts to fail the test systematically.
As far as testing is concerned, most users who are not specialists in random numbers will not want to choose from among the many statistical tests available, set parameters for each one and apply them serially; i.e., most users will not be concerned with (2) above. Rather, most users will want to use the pre-programmed batteries of tests (3) to test the RNGs that are used in their statistical packages. To satisfy the needs of such users, TESTU01 offers several batteries of tests including ‘Small Crush’ (which consists of 10 tests), ‘Crush’ (96 tests) and ‘Big Crush’ (106 tests). The specific tests applied by each battery are given in the User Guide. On a 1.7 GHz Pentium 4 running Red Hat Linux 9.0, for a simple RNG, Small Crush takes about 2 minutes. Crush takes about 1.7 hours. Big Crush takes about 12 hours. (For a more complex RNG, all these times increase by a factor of two or more.) By contrast, the DIEHARD tests take about 15 seconds to run.