niederreiter¶

The niederreiter generator is a 32-bit Gray code-based quasi-random number generator.

Description

According to results of Bratley, Fox and Niederreiter [Bratley92] Niederreiter sequences have the best known theoretical asymptotic properties. The default dimension of quasi-random vectors can vary from 1 to 318 inclusive. It is also allowed to register user-defined parameters (irreducible polynomials).

Generation algorithm

$x_{n} = x_{n_{1}} \oplus v_{c}$

$u_{n} = x_{n} / 2^{32}$

The value $c$ is the right-most zero bit in $n - 1$ ; $x_{n}$ is s-dimensional vector of 32-bit values. The s-dimensional vectors (calculated during engine initialization) $v_{i}, i = 1, 32$ are called direction numbers. The vector $u_{n}$ is the generator output normalized to the unit hypercube $(0, 1)^{s}$ .

class niederreiter¶

Syntax

namespace oneapi::mkl::rng {
class niederreiter {
public:
    static constexpr std::uint32_t default_dimensions_number = 1;

    niederreiter(sycl::queue queue, std::uint32_t dimensions = default_dimensions_number);

    niederreiter(sycl::queue queue, std::vector<std::uint32_t>& irred_polynomials);

    niederreiter(const niederreiter& other);

    niederreiter(niederreiter&& other);

    niederreiter& operator=(const niederreiter& other);

    niederreiter& operator=(niederreiter&& other);

    ~niederreiter();
};
}

Class Members

Routine	Description
niederreiter(sycl::queue queue, std::uint32_t dimensions = default_dimensions_number)	Constructor with specified number of dimensions. The value should be $1. .318$ .
niederreiter(sycl::queue queue, std::vector<std::uint32_t>& irred_polynomials)	Constructor for extended use-case, when it’s needed to use the number of dimensions greater than 318 or obtain another sequence.
niederreiter(const niederreiter& other)	Copy constructor
niederreiter(niederreiter&& other)	Move constructor
niederreiter& operator=(const niederreiter& other)	Copy assignment operator
niederreiter& operator=(niederreiter&& other)	Move assignment operator

Constructors

niederreiter::niederreiter(sycl::queue queue, std::uint32_t dimensions = default_dimensions_number)

Input Parameters

queue: Valid sycl::queue object, calls of the oneapi::mkl::rng::generate() routine submits kernels in this queue to obtain random numbers from a given engine.
dimensions: Number of dimensions. If $d i m e n < 1$ or $d i m e n > 318$ , assume $d i m e n = 1$ .

niederreiter::niederreiter(sycl::queue queue, std::vector<std::uint32_t>& irred_polynomials)

Input Parameters

queue: Valid sycl::queue object, calls of the oneapi::mkl::rng::generate() routine submits kernels in this queue to obtain random numbers from a given engine.
irred_polynomials: If you want to generate quasi-random vectors of greater dimension or obtain another sequence, you can register a set of your own irreducible polynomials. The number of dimensions corresponds to the length of the vector.

niederreiter::niederreiter(const niederreiter& other)

Input Parameters

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

niederreiter::niederreiter(niederreiter&& other)

Input Parameters

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

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

Input Parameters

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

niederreiter::niederreiter& operator=(niederreiter&& other)

Input Parameters

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

Parent topic: Engines (Basic Random Number Generators)

oneAPI Specification 1.1-rev-1 documentation

niederreiter¶

class niederreiter¶