wichmann_hill

wichmann_hill#

The wichmann_hill engine is the set of 273 Wichmann-Hill’s combined multiplicative congruential generators from NAG Numerical Libraries [NAG].

Description

The set of 372 different basic pseudorandom number generators wichmann_hill is the second basic generator in the NAG libraries.

Generation algorithm

$x_{n} = a_{1, j} x_{n - 1} (m o d m_{1, j})$

$y_{n} = a_{2, j} y_{n - 1} (m o d m_{2, j})$

$z_{n} = a_{3, j} z_{n - 1} (m o d m_{3, j})$

$w_{n} = a_{4, j} w_{n - 1} (m o d m_{4, j})$

$u_{n} = (x_{n} / m_{1, j} + y_{n} / m_{2, j} + z_{n} / m_{3, j} + w_{n} / m_{4, j}) m o d 1$

The constants $a_{i, j}$ range from 112 to 127, the constants $m_{i, j}$ are prime numbers ranging from 16718909 to 16776917, close to $2^{24}$ .

class wichmann_hill#

Syntax

namespace oneapi::mkl::rng {
class wichmann_hill {
public:
    static constexpr std::uint32_t default_seed = 1;

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

    wichmann_hill(sycl::queue queue, std::uint32_t seed, std::uint32_t engine_idx);

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

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

    wichmann_hill(const wichmann_hill& other);

    wichmann_hill(wichmann_hill&& other);

    wichmann_hill& operator=(const wichmann_hill& other);

    wichmann_hill& operator=(wichmann_hill&& other);

    ~wichmann_hill();
};
}

Class Members

Routine	Description
wichmann_hill(sycl::queue queue, std::uint32_t seed = default_seed)	Constructor for common seed initialization of the engine (for this case multiple generators of the set would be used)
wichmann_hill(sycl::queue queue, std::uint32_t seed, std::uint32_t engine_idx)	Constructor for common seed initialization of the engine (for this case single generator of the set would be used)
wichmann_hill(sycl::queue& queue, std::initializer_list<std::uint32_t> seed)	Constructor for extended seed initialization of the engine (for this case multiple generators of the set would be used)
wichmann_hill(sycl::queue& queue, std::initializer_list<std::uint32_t> seed, std::uint32_t engine_idx)	Constructor for extended seed initialization of the engine (for this case single generator of the set would be used)
wichmann_hill(const wichmann_hill& other)	Copy constructor
wichmann_hill(wichmann_hill&& other)	Move constructor
wichmann_hill& operator=(const wichmann_hill& other)	Copy assignment operator
wichmann_hill& operator=(wichmann_hill&& other)	Move assignment operator

Constructors

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

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.
seed: The initial conditions of the generator state. Assume $x_{0} = s e e d m o d m_{1}, y_{0} = z_{0} = w_{0} = 1$ . If $x_{0} = 0$ , assume $x_{0} = 1$ .

wichmann_hill::wichmann_hill(sycl::queue queue, std::uint32_t seed, std::uint32_t engine_idx)

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.
seed: The initial conditions of the generator state. Assume $x_{0} = s e e d m o d m_{1}, y_{0} = z_{0} = w_{0} = 1$ . If $x_{0} = 0$ , assume $x_{0} = 1$ .
engine_idx: The index of the set 1, …, 273.

Throws

oneapi::mkl::invalid_argument: Exception is thrown when $i d x > 273$

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

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.

seed

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

if $n = 1 : x_{0} = s e e d [0] m o d m_{1}, y_{0} = z_{0} = w_{0} = 1$ . If $x_{0} = 0$ , assume $x_{0} = 1$ .

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

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

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

$z_{0} = s e e d [2] m o d m_{3}, w_{0} = s e e d [3] m o d m_{4}$ .

wichmann_hill::wichmann_hill(sycl::queue& queue, std::initializer_list<std::uint32_t> seed, std::uint32_t engine_idx)

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.

seed

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

if $n = 1 : x_{0} = s e e d [0] m o d m_{1}, y_{0} = z_{0} = w_{0} = 1$ . If $x_{0} = 0$ , assume $x_{0} = 1$ .

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

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

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

$z_{0} = s e e d [2] m o d m_{3}, w_{0} = s e e d [3] m o d m_{4}$ .

engine_idx

The index of the set 1, …, 273.

wichmann_hill::wichmann_hill(const wichmann_hill& other)

Input Parameters

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

wichmann_hill::wichmann_hill(wichmann_hill&& other)

Input Parameters

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

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

Input Parameters

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

wichmann_hill::wichmann_hill& operator=(wichmann_hill&& other)

Input Parameters

other: Valid wichmann_hill 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)

wichmann_hill

Contents

wichmann_hill#

class wichmann_hill#