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::mkl::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)

mrg32k3a

Contents

mrg32k3a#

class mrg32k3a#