mrg32k3a

Contents

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

\(x_n=a_{11} x_{n-1} + a_{12} x_{n-2} + a_{13} x_{n-3}(mod \ m_{1})\)

\(y_n = a_{21} y_{n-1} + a_{22} y_{n-2} + a_{23} (mod \ m_2)\)

\(z_n = x_n - y_n (mod \ m_{1})\)

\(u_n = z_n / m_1\)

\(a_{11} = 0, a_{12} = 1403580, a_{13} = -810728, m_1 = 2^{32} - 209\)

\(a_{21} = 527612, a_{22} = 0, a_{23} = -1370589, m_2 = 2^{32} - 22853\)

class mrg32k3a#

Syntax

namespace oneapi::math::rng::device {
  template<std::int32_t VecSize = 1>
  class mrg32k3a {
  public:
    static constexpr std::uint32_t default_seed = 1;
    static constexpr std::int32_t vec_size = VecSize;

    mrg32k3a();
    mrg32k3a(std::uint32_t seed, std::uint64_t offset = 0);
    mrg32k3a(std::initializer_list<std::uint32_t> seed, std::uint64_t offset = 0);
    mrg32k3a(std::uint32_t seed, std::initializer_list<std::uint64_t> offset);
    mrg32k3a(std::initializer_list<std::uint32_t> seed, std::initializer_list<std::uint64_t> offset);
  };
}

Class Template Parameters

VecSize

Describes the size of vector which will be produced by generate function by this engine. VecSize values may be 1, 2, 3, 4, 8, 16 as sycl::vec class size. By default VecSize = 1, for this case, a single random number is returned by the generate function.

Class Members

Routine

Description

mrg32k3a()

Default constructor

mrg32k3a(std::uint32_t seed, std::uint64_t offset = 0)

Constructor for common seed initialization of the engine and common number of skipped elements

mrg32k3a(std::initializer_list<std::uint32_t> seed, std::uint64_t offset = 0)

Constructor for extended seed initialization of the engine and common number of skipped elements

mrg32k3a(std::uint32_t seed, std::initializer_list<std::uint64_t> offset)

Constructor for common seed initialization of the engine and extended number of skipped elements

mrg32k3a(std::initializer_list<std::uint32_t> seed, std::initializer_list<std::uint64_t> offset)

Constructor for extended seed initialization of the engine and extended number of skipped elements

Constructors

mrg32k3a::mrg32k3a()
mrg32k3a::mrg32k3a(std::uint32_t seed, std::uint64_t offset = 0)

Input Parameters

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 \(n = 1: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = x_{-1} = y_{-3} = y_{-2} = y_{-1} = 1\)

if \(n = 2: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = y_{-3} = y_{-2} = y_{-1} = 1\)

if \(n = 3: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = seed[2] \ mod \ m_1\)

\(y_{-3} = y_{-2} = y_{-1} = 1\)

if \(n = 4: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = seed[2] \ mod \ m_1\)

\(y_{-3} = seed[3] \ mod \ m_2, y_{-2} = y_{-1} = 1\)

if \(n = 5: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = seed[2] \ mod \ m_1\)

\(y_{-3} = seed[3] \ mod \ m_2, y_{-2} = seed[4] \ mod \ m_2, y_{-1} = 1\)

if \(n \geqslant 6: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = seed[2] \ mod \ m_1\)

\(y_{-3} = seed[3] \ mod \ m_2, y_{-2} = seed[4] \ mod \ m_2, y_{-1} = seed[5] \ mod \ m_2\)

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 \(y_{-3} = 1\).

offset

Number of skipped elements.

mrg32k3a::mrg32k3a(std::initializer_list<std::uint32_t> seed, std::uint64_t offset = 0)

Input Parameters

seed

Initial conditions of the engine state.

offset

Number of skipped elements.

mrg32k3a::mrg32k3a(std::uint32_t seed, std::initializer_list<std::uint64_t> offset)

Input Parameters

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 \(n = 1: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = x_{-1} = y_{-3} = y_{-2} = y_{-1} = 1\)

if \(n = 2: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = y_{-3} = y_{-2} = y_{-1} = 1\)

if \(n = 3: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = seed[2] \ mod \ m_1\)

\(y_{-3} = y_{-2} = y_{-1} = 1\)

if \(n = 4: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = seed[2] \ mod \ m_1\)

\(y_{-3} = seed[3] \ mod \ m_2, y_{-2} = y_{-1} = 1\)

if \(n = 5: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = seed[2] \ mod \ m_1\)

\(y_{-3} = seed[3] \ mod \ m_2, y_{-2} = seed[4] \ mod \ m_2, y_{-1} = 1\)

if \(n \geqslant 6: x_{-3} = seed[0] \ mod \ m_1, x_{-2} = seed[1] \ mod \ m_1, x_{-1} = seed[2] \ mod \ m_1\)

\(y_{-3} = seed[3] \ mod \ m_2, y_{-2} = seed[4] \ mod \ m_2, y_{-1} = seed[5] \ mod \ m_2\)

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 \(y_{-3} = 1\).

offset

Number of skipped elements. Offset is calculated as: num_to_skip [0]+ num_to_skip [1]*264 + num_to_skip [2]* 2128 + … + num_to_skip [n-1]*264 *(n-1).

mrg32k3a::mrg32k3a(std::initializer_list<std::uint32_t> seed, std::initializer_list<std::uint64_t> offset)

Input Parameters

seed

Initial conditions of the engine state.

offset

Number of skipped elements. Offset is calculated as: num_to_skip [0]+ num_to_skip [1]*264 + num_to_skip [2]* 2128 + … + num_to_skip [n-1]*264 *(n-1).

Parent topic: Device Engines (Basic Random Number Generators)