# Basic Generators

VSL provides the following BRNGs, which differ in speed and other properties:

- the 32-bit multiplicative congruential pseudorandom number generator `MCG(1132489760, 231 -1)` [L’Ecuyer99]

- the 32-bit generalized feedback shift register pseudorandom number generator `GFSR(250,103)` [Kirkpatrick81]

- the combined multiple recursive pseudorandom number generator `MRG-32k3a` [L’Ecuyer99a]

- the 59-bit multiplicative congruential pseudorandom number generator `MCG(1313, 259)` from NAG Numerical Libraries [NAG]

- Wichmann-Hill pseudorandom number generator (a set of 273 basic generators) from NAG Numerical Libraries [NAG]

- Mersenne Twister pseudorandom number generator `MT19937` [Matsumoto98] with period length 219937-1 of the produced sequence

- Set of 1024 Mersenne Twister pseudorandom number generators `MT2203` [Matsumoto98], [Matsumoto00]. Each of them generates a sequence of period length equal to 22203-1. Parameters of the generators provide mutual independence of the corresponding sequences.

Besides these pseudorandom number generators, VSL provides two basic quasi-random number generators:

- Sobol quasi-number generator [Sobol76], [Bratley88], which works in arbitrary dimension. For dimensions greater than 40 the user should supply initialization parameters (initial direction numbers and primitive polynomials or direction numbers) by using vslNewStreamEx function. See additional details on interface for registration of the parameters in the library in VSL Notes.

- Niederreiter quasi-random number generator [Bratley92], which works in arbitrary dimension. For dimensions greater than 318 the user should supply initialization parameters (irreducible polynomials or direction numbers) by using vslNewStreamEx function. See additional details on interface for registration of the parameters in the library in VSL Notes.

Aslo see some testing results for the generators in VSL Notes and comparative performance data at http://www.intel.com/software/products/mkl/data/vsl/vsl_performance_data.htm.

VSL provides means of registration of such user-designed generators through the steps described in Advanced Service Subroutines.

For some basic generators, VSL provides two methods of creating independent random streams in multiprocessor computations, which are the leapfrog method and the block-splitting method. These sequence splitting methods are also useful in sequential Monte Carlo.

In addition, MT2203 pseudorandom number generator is a set of 1024 generators designed to create up to 1024 independent random sequences, which might be used in parallel Monte Carlo simulations. Another generator that has the same feature is Wichmann-Hill. It allows creating up to 273 independent random streams. The properties of the generators designed for parallel computations are discussed in detail in [Coddington94].

You may want to design and use your own basic generators. VSL provides means of registration of such user-designed generators through the steps described in Advanced Service Subroutines.

There is also an option to utilize externally generated random numbers in VSL distribution generator routines. For this purpose VSL provides three additional basic random number generators:

- for external random data packed in 32-bit integer array

- for external random data stored in double precision floating-point array; data is supposed to be uniformly distributed over (a,b) interval

- for external random data stored in single precision floating-point array; data is supposed to be uniformly distributed over (a,b) interval.

Such basic generators are called the abstract basic random number generators.

See VSL Notes for a more detailed description of the generator properties.

- BRNG Parameter Definition
- Random Streams
- Data Types

Parent topic: Random Number Generators