mrg32k3a#

The combined multiple recursive pseudorandom number generator MRG32k3a.

Description

MRG32k3a engine is a 32-bit combined multiple recursive generator with two components of order 3 [L’Ecuyer99a]. MRG32k3a combined generator meets the requirements for modern RNGs, such as good multidimensional uniformity, or a long period ( $p \approx 2^{191}$ ).

Generation algorithm

$x_{n} = a_{11} x_{n - 1} + a_{12} x_{n - 2} + a_{13} x_{n - 3} (m o d m_{1})$

$y_{n} = a_{21} y_{n - 1} + a_{22} y_{n - 2} + a_{23} (m o d m_{2})$

$z_{n} = x_{n} - y_{n} (m o d m_{1})$

$u_{n} = z_{n} / m_{1}$

$a_{11} = 0, a_{12} = 1403580, a_{13} = - 810728, m_{1} = 2^{32} - 209$

$a_{21} = 527612, a_{22} = 0, a_{23} = - 1370589, m_{2} = 2^{32} - 22853$

class mrg32k3a#

Syntax

namespace oneapi::math::rng {
class mrg32k3a {
public:
    static constexpr std::uint32_t default_seed = 1;

    mrg32k3a(sycl::queue queue, std::uint32_t seed = default_seed);

    mrg32k3a(sycl::queue queue, std::initializer_list<std::uint32_t> seed);

    mrg32k3a(const mrg32k3a& other);

    mrg32k3a(mrg32k3a&& other);

    mrg32k3a& operator=(const mrg32k3a& other);

    mrg32k3a& operator=(mrg32k3a&& other);

    ~mrg32k3a();
};
}

Class Members

Routine	Description
mrg32k3a(sycl::queue queue, std::uint32_t seed = default_seed)	Constructor for common seed initialization of the engine
mrg32k3a(sycl::queue queue, std::initializer_list<std::uint32_t> seed)	Constructor for extended seed initialization of the engine
mrg32k3a(const mrg32k3a& other)	Copy constructor
mrg32k3a(mrg32k3a&& other)	Move constructor
mrg32k3a& operator=(const mrg32k3a& other)	Copy assignment operator
mrg32k3a& operator=(mrg32k3a&& other)	Move assignment operator

Constructors

mrg32k3a::mrg32k3a(sycl::queue queue, std::uint32_t seed = default_seed)

Input Parameters

queue: Valid sycl::queue object, calls of the oneapi::math::rng::generate() routine submits kernels in this queue to obtain random numbers from a given engine.
seed: The initial conditions of the generator state, assume $x_{- 3} = s e e d m o d m_{1}, x_{- 2} = x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$ .

mrg32k3a::mrg32k3a(sycl::queue queue, std::initializer_list<std::uint32_t> seed)

Input Parameters

queue

Valid sycl::queue object, calls of the oneapi::math::rng::generate() routine submits kernels in this queue to obtain random numbers from a given engine.

seed

The initial conditions of the generator state, assume if $n = 0 : x_{- 3} = x_{- 2} = x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 1 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 2 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 3 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = y_{- 2} = y_{- 1} = 1$

if $n = 4 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = s e e d [3] m o d m_{2}, y_{- 2} = y_{- 1} = 1$

if $n = 5 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = s e e d [3] m o d m_{2}, y_{- 2} = s e e d [4] m o d m_{2}, y_{- 1} = 1$

if $n ⩾ 6 : x_{- 3} = s e e d [0] m o d m_{1}, x_{- 2} = s e e d [1] m o d m_{1}, x_{- 1} = s e e d [2] m o d m_{1}$

$y_{- 3} = s e e d [3] m o d m_{2}, y_{- 2} = s e e d [4] m o d m_{2}, y_{- 1} = s e e d [5] m o d m_{2}$

if the values prove to be $x_{- 3} = x_{- 2} = x_{- 1} = 0$ , assume $x_{- 3} = 1$

if the values prove to be $y_{- 3} = y_{- 2} = y_{- 1} = 0$ , assume $y_{- 3} = 1$

mrg32k3a::mrg32k3a(const mrg32k3a& other)

Input Parameters

other: Valid mrg32k3a object. The queue and state of the other engine is copied and applied to the current engine.

mrg32k3a::mrg32k3a(mrg32k3a&& other)

Input Parameters

other: Valid mrg32k3a object. The queue and state of the other engine is moved to the current engine.

mrg32k3a::mrg32k3a& operator=(const mrg32k3a& other)

Input Parameters

other: Valid mrg32k3a object. The queue and state of the other engine is copied and applied to the current engine.

mrg32k3a::mrg32k3a& operator=(mrg32k3a&& other)

Input Parameters

other: Valid mrg32k3a r-value object. The queue and state of the other engine is moved to the current engine.

Parent topic: Host Engines (Basic Random Number Generators)

mrg32k3a

Contents

mrg32k3a#

class mrg32k3a#