# Uniform Random GeneratorΒΆ

Generating simulations according to a distribution is based on
generating simulations according to a Uniform distribution on
: several techniques exist then to transform a
realization according to a uniform distribution onto a realization
according to a distribution which cumulative distribution function is
(refer to for each distribution).

Thus, the quality of the random generation of simulation is entirely
based on the quality of the

*deterministic*algorithm which simulates realizations of the Uniform(0,1) distribution.We use the DSFTM algorithm described here, which is the
acronym of

**D**ouble precision**S**IMD oriented**F**ast**M**ersenne**T**wister.Each character is detailed of the acronym is detailed :

**S = SIMD = Single Instruction Multiple Data**: the DSFMT algorithm is able to detect and take profit of the capacity of the microprocessor to realise several operations at a time.**F = Fast**: the transformation of the -th state vector of the random generator into the -th state vector is written in order to optimize its performance.**MT = Mersenne Twister**: the algorithm characteristics are the following ones :- the algorithm is initialized with a high Mersenne Number, of type , with .
- the algorithm period depends on that initial point : . As a general way, the bad effects of the periodicity of the algorithm arise as soon as the number of simulations is greater than simulations. Here, we have : .
- the realizations of the DSFMT algorithm are uniformly distributed within until .

API:

- See
`RandomGenerator`

- See
`RandomGeneratorState`

to save the generator state

Examples: