# rand

### MODULE

### MODULE SUMMARY

### DESCRIPTION

This module provides a random number generator. The module contains a number of algorithms. The uniform distribution algorithms use the scrambled Xorshift algorithms by Sebastiano Vigna. The normal distribution algorithm uses the Ziggurat Method by Marsaglia and Tsang.

For some algorithms, jump functions are provided for generating non-overlapping sequences for parallel computations. The jump functions perform calculations equivalent to perform a large number of repeated calls for calculating new states.

The following algorithms are provided:

**exsplus**-
Xorshift116+, 58 bits precision and period of 2^116-1

Jump function: equivalent to 2^64 calls

**exs64**-
Xorshift64*, 64 bits precision and a period of 2^64-1

Jump function: not available

**exs1024**-
Xorshift1024*, 64 bits precision and a period of 2^1024-1

Jump function: equivalent to 2^512 calls

The default algorithm is exsplus. If a specific algorithm is required, ensure to always use seed/1 to initialize the state.

Every time a random number is requested, a state is used to calculate it and a new state is produced. The state can either be implicit or be an explicit argument and return value.

The functions with implicit state use the process dictionary variable rand_seed to remember the current state.

If a process calls uniform/0 or uniform/1 without setting a seed first, seed/1 is called automatically with the default algorithm and creates a non-constant seed.

The functions with explicit state never use the process dictionary.

**Examples:**

Simple use; creates and seeds the default algorithm with a non-constant seed if not already done:

R0 = rand:uniform(), R1 = rand:uniform(),

Use a specified algorithm:

_ = rand:seed(exs1024), R2 = rand:uniform(),

Use a specified algorithm with a constant seed:

_ = rand:seed(exs1024, {123, 123534, 345345}), R3 = rand:uniform(),

Use the functional API with a non-constant seed:

S0 = rand:seed_s(exsplus), {R4, S1} = rand:uniform_s(S0),

Create a standard normal deviate:

{SND0, S2} = rand:normal_s(S1),

This random number generator is not cryptographically strong. If a strong cryptographic random number generator is needed, use one of functions in the crypto module, for example, crypto:strong_rand_bytes/1.

### DATA TYPES

alg() = exs64 | exsplus | exs1024

Algorithm-dependent state.

Algorithm-dependent state that can be printed or saved to file.

### EXPORTS

export_seed() -> undefined | export_state()

Returns the random number state in an external format. To be used with seed/1.

export_seed_s(X1 :: state()) -> export_state()

Returns the random number generator state in an external format. To be used with seed/1.

jump() -> NewS :: state()

Returns the state after performing jump calculation to the state in the process dictionary.

This function generates a not_implemented error exception when the jump function is not implemented for the algorithm specified in the state in the process dictionary.

jump(State :: state()) -> NewS :: state()

Returns the state after performing jump calculation to the given state.

This function generates a not_implemented error exception when the jump function is not implemented for the algorithm specified in the state.

Returns a standard normal deviate float (that is, the mean is 0 and the standard deviation is 1) and updates the state in the process dictionary.

normal_s(State0 :: state()) -> {float(), NewS :: state()}

Returns, for a specified state, a standard normal deviate float (that is, the mean is 0 and the standard deviation is 1) and a new state.

seed(AlgOrExpState :: alg() | export_state()) -> state()

Seeds random number generation with the specifed algorithm and time-dependent data if AlgOrExpState is an algorithm.

Otherwise recreates the exported seed in the process dictionary, and returns the state. See also export_seed/0.

seed(Alg :: alg(), S0 :: {integer(), integer(), integer()}) ->

state()

Seeds random number generation with the specified algorithm and integers in the process dictionary and returns the state.

seed_s(AlgOrExpState :: alg() | export_state()) -> state()

Seeds random number generation with the specifed algorithm and time-dependent data if AlgOrExpState is an algorithm.

Otherwise recreates the exported seed and returns the state. See also export_seed/0.

seed_s(Alg :: alg(), S0 :: {integer(), integer(), integer()}) ->

state()

Seeds random number generation with the specified algorithm and integers and returns the state.

Returns a random float uniformly distributed in the value range 0.0 < X < 1.0 and updates the state in the process dictionary.

uniform(N :: integer() >= 1) -> X :: integer() >= 1

Returns, for a specified integer N >= 1, a random integer uniformly distributed in the value range 1 <= X <= N and updates the state in the process dictionary.

uniform_s(State :: state()) -> {X :: float(), NewS :: state()}

Returns, for a specified state, random float uniformly distributed in the value range 0.0 < X < 1.0 and a new state.

uniform_s(N :: integer() >= 1, State :: state()) ->

{X :: integer() >= 1, NewS :: state()}

Returns, for a specified integer N >= 1 and a state, a random integer uniformly distributed in the value range 1 <= X <= N and a new state.